1
00:00:00,870 --> 00:00:04,710
Students, welcome to the section where we deal with circles.

2
00:00:04,950 --> 00:00:06,810
Let's get started with the basics.

3
00:00:07,170 --> 00:00:08,960
Let's take an example of a circle.

4
00:00:09,270 --> 00:00:12,090
So this type of a shape is called a circle.

5
00:00:12,330 --> 00:00:15,800
You can see that it is a simple closed curve, right?

6
00:00:15,960 --> 00:00:17,520
Remember, simple means.

7
00:00:17,520 --> 00:00:21,300
It does not cross itself and closed means it's not open.

8
00:00:21,570 --> 00:00:22,040
All right.

9
00:00:22,230 --> 00:00:29,570
Now, in this circle, you can see that every point on the circle is at an equal distance from the center.

10
00:00:29,940 --> 00:00:34,070
So that's the defining characteristic of a circle over here.

11
00:00:34,080 --> 00:00:35,690
This is the center of the circle.

12
00:00:35,910 --> 00:00:42,990
And you can see that every point on the circle, that is all these points are at the same distance from

13
00:00:42,990 --> 00:00:43,740
the center.

14
00:00:43,920 --> 00:00:46,580
So let's take a few points on this circle.

15
00:00:46,950 --> 00:00:51,390
So we have point A, B, B and E taken on the circle.

16
00:00:51,660 --> 00:00:53,850
So what have we learned over here?

17
00:00:54,030 --> 00:00:59,840
We have seen that if we join these points to the center, then these lengths are equal.

18
00:01:00,030 --> 00:01:02,310
That is C is equal to see.

19
00:01:02,310 --> 00:01:04,590
B is equal to the galaxy.

20
00:01:04,980 --> 00:01:05,430
All right.

21
00:01:05,580 --> 00:01:06,920
Now let's take one of them.

22
00:01:07,050 --> 00:01:12,990
So let's take for example, see, now this length is called the radius of the circle.

23
00:01:13,290 --> 00:01:16,290
Now, over here, the radius is the singular.

24
00:01:16,470 --> 00:01:20,600
Now, if you take multiple radius, as you call it, really, I'm all right.

25
00:01:20,790 --> 00:01:25,340
Now, let's take the radius as are now over here.

26
00:01:25,500 --> 00:01:31,090
If you observe E, this is a line segment that passes through the center.

27
00:01:31,320 --> 00:01:35,520
So this type of a nine segment is called the diameter of the Circle.

28
00:01:35,700 --> 00:01:43,810
And that's equal to two times are right because it C is equal to are and C is also equal to up to 80

29
00:01:43,860 --> 00:01:46,090
is equal to two times are now.

30
00:01:46,170 --> 00:01:51,600
Earlier we had learned that in the case of a line, you just need two points, right, to define a line

31
00:01:51,780 --> 00:01:55,680
because through two given points, only one line can be drawn.

32
00:01:55,770 --> 00:02:01,680
Right now if you take just two points, you will see that you can draw multiple circles through two

33
00:02:01,680 --> 00:02:09,240
given points to define a unique circle, you will need three points so only one circle can be drawn

34
00:02:09,450 --> 00:02:14,610
through three given points already having established the basics of a circle.

35
00:02:14,790 --> 00:02:20,400
Let's move on and learn some of the important terms in the case of circles.

36
00:02:20,700 --> 00:02:21,080
All right.

37
00:02:21,240 --> 00:02:22,440
We start with the card.

38
00:02:22,840 --> 00:02:24,680
Now, this is an example of a card.

39
00:02:24,720 --> 00:02:25,650
This is called P.

40
00:02:25,650 --> 00:02:29,970
Q that is a card connects two points on the circle.

41
00:02:30,360 --> 00:02:36,150
Now, if these were extended and if it's like a line segment like this, then you can call this second.

42
00:02:38,000 --> 00:02:46,430
All right, now let's press on over here, let me take any two points on this circle at this point and

43
00:02:46,430 --> 00:02:51,580
point B now this measure over here is what you call an arc.

44
00:02:51,620 --> 00:02:52,640
This is the arc.

45
00:02:52,820 --> 00:02:55,120
That is it is a portion of the circle.

46
00:02:55,130 --> 00:02:56,520
It's a portion of the circle.

47
00:02:56,870 --> 00:02:57,350
All right.

48
00:02:57,530 --> 00:03:00,140
Now, over here, you can see that this is the minor arc.

49
00:03:00,350 --> 00:03:04,790
And if you draw it like this, this would have been called the major arc, Abe.

50
00:03:05,240 --> 00:03:05,750
All right.

51
00:03:06,320 --> 00:03:09,770
So we have a minor arc and we have a major arc.

52
00:03:11,020 --> 00:03:15,830
So the minor one is a smaller one and the major one is the bigger one, this part over here.

53
00:03:16,150 --> 00:03:24,400
All right, now you the northern arc, either by writing arc or you have this type of a shape over here.

54
00:03:24,760 --> 00:03:25,170
All right.

55
00:03:25,420 --> 00:03:27,150
Now, let's move on to a sector.

56
00:03:27,340 --> 00:03:29,040
What is a sector of a circle?

57
00:03:29,260 --> 00:03:34,390
It's an area enclosed by an arc and a pair of radiate.

58
00:03:34,690 --> 00:03:35,610
But what does that mean?

59
00:03:35,620 --> 00:03:36,730
Let's take an example.

60
00:03:36,920 --> 00:03:41,220
It's enclosed by a pair of really and it's enclosed by an arc.

61
00:03:41,230 --> 00:03:43,840
We know what radiuses and we know what an arc is.

62
00:03:44,110 --> 00:03:45,940
So let's combine these two together.

63
00:03:46,240 --> 00:03:49,670
So this area, for example, is called a sector.

64
00:03:50,440 --> 00:03:50,900
All right.

65
00:03:51,190 --> 00:03:52,810
Now let's move on to segment.

66
00:03:53,110 --> 00:03:54,070
What is a segment?

67
00:03:54,400 --> 00:03:58,490
A segment is an area enclosed by a code and anarch.

68
00:03:58,730 --> 00:03:59,980
So we know what the code is.

69
00:03:59,980 --> 00:04:01,120
We've learned that over here.

70
00:04:01,120 --> 00:04:01,450
Right.

71
00:04:01,660 --> 00:04:03,700
And we know what an ark is.

72
00:04:03,700 --> 00:04:06,060
We have seen this is, for example, an ark.

73
00:04:06,250 --> 00:04:08,110
But let's combine these two together.

74
00:04:08,380 --> 00:04:10,830
So over here you have a segment.

75
00:04:10,840 --> 00:04:11,860
So this is a segment.

76
00:04:12,040 --> 00:04:18,310
Now, remember, as in the case of an ark, you have a minor ark and major arc over here.

77
00:04:18,310 --> 00:04:23,330
Also, you have a minor sector and you have a major sector.

78
00:04:23,350 --> 00:04:24,550
This is the minor sector.

79
00:04:27,160 --> 00:04:31,760
OK, and over here also you have a minor segment.

80
00:04:31,810 --> 00:04:33,100
This is the minor segment.

81
00:04:34,620 --> 00:04:40,710
Let me write that over here and this pot over here, the outside of the circle, that would be the major

82
00:04:40,710 --> 00:04:41,300
segment.

83
00:04:41,640 --> 00:04:43,710
All right, now let's move on.

84
00:04:43,980 --> 00:04:46,920
What is the circumference of a circle?

85
00:04:46,950 --> 00:04:48,270
What does that mean?

86
00:04:48,520 --> 00:04:51,990
It's equivalent to the perimeter of polygons, right?

87
00:04:51,990 --> 00:04:54,670
For example, in the case of a rectangle or square.

88
00:04:54,690 --> 00:04:58,350
We have seen that if you add the length of the borders, you get perimeter.

89
00:04:58,350 --> 00:04:58,610
Right.

90
00:04:58,830 --> 00:05:02,330
The same thing in the case of a circle is called circumference.

91
00:05:02,640 --> 00:05:05,430
So it's the distance around a circle.

92
00:05:05,640 --> 00:05:08,030
For example, over here I have another circle.

93
00:05:08,190 --> 00:05:14,700
If I move around it one time, this length over here is called the circumference of the circle.

94
00:05:15,000 --> 00:05:17,250
Now, over here, this is the center of the circle.

95
00:05:17,460 --> 00:05:19,600
Let me draw a line through the center.

96
00:05:19,860 --> 00:05:23,570
Now, you can see that this line over here is a diameter.

97
00:05:23,580 --> 00:05:24,720
We have already seen that.

98
00:05:24,870 --> 00:05:30,270
And you can observe that the diameter divides a circle into two equal parts.

99
00:05:31,140 --> 00:05:34,730
So this part over here and this part of here is of the same area.

100
00:05:34,740 --> 00:05:38,790
So the diameter divides a circle into two equal parts.

101
00:05:39,030 --> 00:05:43,830
Now, if you take one such part, that is what we call a semicircle.

102
00:05:44,040 --> 00:05:44,460
All right.

103
00:05:44,460 --> 00:05:48,210
Let's quickly revise what we've learned in terms of terms in this section.

104
00:05:48,480 --> 00:05:52,020
We have learned that a cord connects two points on the circle.

105
00:05:52,200 --> 00:05:53,220
So, for example, P.

106
00:05:53,220 --> 00:05:54,260
Q is a cord.

107
00:05:54,510 --> 00:06:01,280
We have seen that an arc is a part of a circle and we have seen that a sector is enclosed by two really,

108
00:06:01,290 --> 00:06:06,740
and an arc and a segment is enclosed by an arc and cord.

109
00:06:07,470 --> 00:06:13,400
We have seen the circumference is the distance around the circle and this is what we call a semicircle.

110
00:06:13,410 --> 00:06:14,970
It's formed by diameter.

111
00:06:15,240 --> 00:06:15,620
All right.

112
00:06:15,750 --> 00:06:19,160
Now let's learn a few more important terms in the case of a circle.

113
00:06:19,830 --> 00:06:24,330
Now, over here, I have a circle and I have arc over here.

114
00:06:24,570 --> 00:06:26,940
Now we start with measure of an arc.

115
00:06:27,360 --> 00:06:29,880
What do we call the measure of this arc?

116
00:06:30,540 --> 00:06:33,940
Let me join A and B to the center of this circle.

117
00:06:34,230 --> 00:06:34,820
All right.

118
00:06:35,040 --> 00:06:40,260
Now, this angle over here is what we call the measure of the minor arc.

119
00:06:40,380 --> 00:06:42,520
Remember, this is the minor arc, right?

120
00:06:42,630 --> 00:06:44,040
This is my in Iraq, Abe.

121
00:06:44,160 --> 00:06:48,740
And therefore the angle substandard by the minor arc at the center.

122
00:06:48,750 --> 00:06:53,310
That is this angle over here is what is called the measure of the minor.

123
00:06:53,580 --> 00:06:57,200
Similarly, this spot over here is the major arc, Abe.

124
00:06:57,240 --> 00:06:57,490
Right.

125
00:06:57,510 --> 00:06:58,320
Let me draw that.

126
00:06:58,710 --> 00:07:02,130
So this part over here is the major arc.

127
00:07:02,130 --> 00:07:09,090
Abe, right now, if you see that this is the angle suspended by the major at the center right.

128
00:07:09,240 --> 00:07:12,660
So that is called the measure of the major arc, Abe.

129
00:07:13,020 --> 00:07:13,490
All right.

130
00:07:13,680 --> 00:07:18,900
Now, an interesting thing to note over here is you will see that if you add these two points, these

131
00:07:18,900 --> 00:07:23,190
two angles together, you get one complete revolution around a point.

132
00:07:23,190 --> 00:07:23,480
Right.

133
00:07:23,670 --> 00:07:29,670
And therefore, this measure plus this measure that is a measure of the major Ebbie, plus the measure

134
00:07:29,670 --> 00:07:33,270
of the minor Abe will give you 360 degrees.

135
00:07:33,690 --> 00:07:34,140
All right.

136
00:07:34,140 --> 00:07:35,020
Let's continue.

137
00:07:35,190 --> 00:07:39,600
We have seen what we mean with the measure of an arc right now.

138
00:07:39,610 --> 00:07:45,480
Let's see what we mean with an inscribed angle in another or the angle supplemented by an arc.

139
00:07:45,660 --> 00:07:47,390
Over here you have arc, Abe.

140
00:07:47,610 --> 00:07:56,700
Now, let's take a point C over here and you see that angle ACB That's this angle over here is the angle

141
00:07:56,700 --> 00:08:00,300
suspended by our Abe at a point, see.

142
00:08:00,730 --> 00:08:01,220
All right.

143
00:08:01,430 --> 00:08:07,470
So this is something that we will see in future lessons also because there is an interesting property

144
00:08:07,470 --> 00:08:08,490
associated with this.

145
00:08:08,640 --> 00:08:10,700
But let me keep that for a future video.

146
00:08:11,010 --> 00:08:11,450
All right.

147
00:08:11,550 --> 00:08:16,450
Now, let's go ahead with understanding various terms of a circle at point C.

148
00:08:16,500 --> 00:08:18,150
Let me draw a tangent.

149
00:08:18,430 --> 00:08:21,750
So that's a tangent at point C, right.

150
00:08:21,790 --> 00:08:25,170
Lynelle is a tangent for L is a tangent to the circle.

151
00:08:25,200 --> 00:08:26,120
Let's see now.

152
00:08:26,130 --> 00:08:27,040
What does that mean?

153
00:08:27,180 --> 00:08:28,260
What is a tangent?

154
00:08:28,380 --> 00:08:32,610
A tangent is a line that touches the circle at only one point.

155
00:08:32,850 --> 00:08:34,470
It can be only at one point.

156
00:08:34,470 --> 00:08:34,670
Right?

157
00:08:34,710 --> 00:08:36,810
It has to be exactly at one point.

158
00:08:37,140 --> 00:08:41,330
Now, if it touches a two points, it would look like this right across this line.

159
00:08:42,480 --> 00:08:49,140
If this line touches the circle at two points over here and here, then this line is called the second.

160
00:08:50,710 --> 00:08:55,690
So we have seen what we mean with a tangent and we have seen what we mean with the second.

161
00:08:55,960 --> 00:08:56,380
All right.

162
00:08:56,530 --> 00:09:01,300
Now let's learn one more interesting thing about tangents over here and at this point all.

163
00:09:01,450 --> 00:09:04,780
And let me correct that two point to point.

164
00:09:04,780 --> 00:09:11,360
Or is the center of this circle and buoyancy is the point at which tangent l touches this circle.

165
00:09:11,500 --> 00:09:18,310
Now, over here you will see that this angle over here, that is the angle formed between the tangent

166
00:09:18,310 --> 00:09:23,680
and the radiate right through the point of intersection of the tangent at the circle.

167
00:09:23,860 --> 00:09:29,920
That angle is equal to 90 degree, but and in that radius form a 90 degree angle.

168
00:09:30,040 --> 00:09:32,110
So that's also a very important property.

169
00:09:32,260 --> 00:09:34,340
And we will see more about that in future.

170
00:09:34,340 --> 00:09:34,780
Reduce.