1 00:00:00,610 --> 00:00:03,910 Let's do this question, a circle with diameter as P. 2 00:00:03,910 --> 00:00:09,820 Q is inscribed inside triangle ABC, the circle meets the triangle at R. 3 00:00:09,850 --> 00:00:13,250 S and Z, always the center of the circle. 4 00:00:13,450 --> 00:00:17,820 This is the point of intersection of argu and B.S. that's over here. 5 00:00:18,220 --> 00:00:20,710 The diameter of the circle is two centimeter. 6 00:00:21,040 --> 00:00:30,270 Find a oh e or if angle puti q b the Q is two times angle s or s or. 7 00:00:30,550 --> 00:00:32,110 All right was the video. 8 00:00:32,260 --> 00:00:34,460 Give it a try and then let's do it together. 9 00:00:35,020 --> 00:00:35,470 All right. 10 00:00:35,470 --> 00:00:35,980 We are back. 11 00:00:35,980 --> 00:00:37,350 I hope you have given it a try. 12 00:00:37,540 --> 00:00:39,850 Let's do it together now. 13 00:00:39,970 --> 00:00:42,460 Let me join our OR and OS. 14 00:00:43,910 --> 00:00:51,320 All right, now, these two angles will be 90 degrees because a is a tangent to the circle and AC is 15 00:00:51,320 --> 00:00:58,680 a tangent to the circle, right, because it's mentioned that this circle is inscribed inside the triangle. 16 00:00:58,700 --> 00:01:02,320 So this is actually the inner circle of triangle ABC. 17 00:01:02,510 --> 00:01:02,850 Right. 18 00:01:02,990 --> 00:01:05,480 And we know that this will be 90 degrees. 19 00:01:05,780 --> 00:01:11,220 And over here, it's also mentioned that the circle meets the triangle at artists and the. 20 00:01:11,270 --> 00:01:11,670 All right. 21 00:01:11,810 --> 00:01:15,050 So these two angles will be 90 degrees right now. 22 00:01:15,230 --> 00:01:16,940 Let's join S and Q. 23 00:01:17,960 --> 00:01:24,560 OK, now you can see that angle, the skew, the askew or angle B skew, both are the same. 24 00:01:24,830 --> 00:01:27,530 They are equal to 90 degree right angle. 25 00:01:27,580 --> 00:01:29,410 Popescu is equal to 90 degrees. 26 00:01:29,600 --> 00:01:30,480 Why is that so. 27 00:01:30,680 --> 00:01:34,190 Because it's the angle sub-standard by the diameter Piku. 28 00:01:34,190 --> 00:01:34,520 Right. 29 00:01:34,820 --> 00:01:38,090 So and you can see that angle dsu an angle. 30 00:01:38,630 --> 00:01:40,880 You are one and the same angle. 31 00:01:41,090 --> 00:01:42,440 So let me write it as angle. 32 00:01:42,440 --> 00:01:45,500 DSU angle is equal to 90 degrees. 33 00:01:45,650 --> 00:01:46,000 Right. 34 00:01:46,190 --> 00:01:48,590 And you can see that angle cube. 35 00:01:48,890 --> 00:01:55,160 That's B the Q this angle over here is an external angle to triangle as the dequeue. 36 00:01:55,160 --> 00:01:55,500 Right. 37 00:01:55,760 --> 00:01:56,360 Why is that. 38 00:01:56,360 --> 00:01:59,990 So you extend D to form this angle over here. 39 00:01:59,990 --> 00:02:01,460 Petechial right now. 40 00:02:01,460 --> 00:02:06,500 Can you remember an important property with respect to triangles and external angles. 41 00:02:06,650 --> 00:02:11,930 Yes, the external angle will be equal to the sum of the internal opposite angles. 42 00:02:11,930 --> 00:02:12,240 Right. 43 00:02:12,500 --> 00:02:20,960 Therefore I can say that Angle Q is equal to 90 degree plus angle is the right y ninety over here because 44 00:02:20,960 --> 00:02:28,700 Bascule is equal to 90 or Priscu is equal to angle DSU plus angle is skewed and instead of angled skua. 45 00:02:28,730 --> 00:02:28,970 Right. 46 00:02:28,970 --> 00:02:37,030 Ninety over here now instead of angle escudo I can write half of angle s or are right. 47 00:02:37,130 --> 00:02:41,860 So that's equal to 90 plus half of angle S or no. 48 00:02:41,870 --> 00:02:42,730 Why is that so. 49 00:02:43,370 --> 00:02:48,120 Well over here you can see s Q D is the same as ESC. 50 00:02:48,140 --> 00:02:56,150 You are right, both of them are this angle and that angle is the angle made by arc are s rated. 51 00:02:56,150 --> 00:03:03,050 It's by Arc Argyris and we know that the angle subtenant by the arc will be half the measure of the 52 00:03:03,050 --> 00:03:03,320 arc. 53 00:03:03,560 --> 00:03:08,290 What is the measure of arc that would be S or are right. 54 00:03:08,450 --> 00:03:11,270 We just need to join these two points to the center. 55 00:03:11,390 --> 00:03:18,590 So Angle s will are is the measure of the arc and s Q D This is the angle subtenant by the arc, so 56 00:03:18,590 --> 00:03:21,950 this will be half the measure of the arc to a right angle. 57 00:03:22,020 --> 00:03:22,910 So are two. 58 00:03:23,120 --> 00:03:29,630 Now this over here is equal to two times angle or because it's given right angle. 59 00:03:29,630 --> 00:03:33,590 Petechia is two times angle s or so that's given. 60 00:03:33,860 --> 00:03:36,500 So therefore I can solve for angle Isaw. 61 00:03:36,680 --> 00:03:42,800 That's three by two angle Asla is equal to ninety degree or angle s or is equal to sixty degrees. 62 00:03:43,070 --> 00:03:44,900 All right, now let's proceed. 63 00:03:45,020 --> 00:03:48,740 You can see that a R or S is forming a kite. 64 00:03:48,740 --> 00:03:49,130 Right. 65 00:03:49,580 --> 00:03:51,470 A R or this is a kite. 66 00:03:51,650 --> 00:03:52,490 Why is that so. 67 00:03:52,790 --> 00:04:00,230 R is equal to S because we are an s are the engines from an external point to a circle and or are is 68 00:04:00,230 --> 00:04:05,000 equal to or less because both of them are radii of this circle right now. 69 00:04:05,000 --> 00:04:09,170 We know that in a kite it has two sets of adjacent sites equal. 70 00:04:09,650 --> 00:04:10,640 Therefore a R. 71 00:04:10,820 --> 00:04:11,710 S is a kite. 72 00:04:11,930 --> 00:04:17,210 Now let me join E and all over here you can see that this is the bigger diagonal. 73 00:04:17,390 --> 00:04:22,040 And in a kite, the bigger diagonal is the angle sector right now. 74 00:04:22,130 --> 00:04:25,940 Over here we got that S or R is equal to sixty degrees. 75 00:04:26,150 --> 00:04:30,710 Therefore this angle over here, D or R will be sixty by two. 76 00:04:30,980 --> 00:04:32,840 That's equal to thirty degrees. 77 00:04:32,840 --> 00:04:33,190 Right. 78 00:04:33,920 --> 00:04:34,390 All right. 79 00:04:34,580 --> 00:04:42,860 Now let's apply our knowledge in trigonometry cos thirty over here will be equal to or divided by equal 80 00:04:42,860 --> 00:04:43,280 right. 81 00:04:43,280 --> 00:04:45,910 So cost thirty is equal to or by equal. 82 00:04:46,180 --> 00:04:47,180 Always the hypotenuse. 83 00:04:47,180 --> 00:04:47,510 Right. 84 00:04:47,750 --> 00:04:50,850 And that's equal to one divided by you. 85 00:04:51,020 --> 00:04:51,420 Right. 86 00:04:51,440 --> 00:04:54,590 Because it's mentioned that the diameter is two centimetre. 87 00:04:54,740 --> 00:04:55,100 Right. 88 00:04:55,400 --> 00:04:59,060 Therefore the radius are all that would be one. 89 00:04:59,060 --> 00:04:59,390 Right. 90 00:04:59,540 --> 00:05:00,830 Therefore the radius is one. 91 00:05:00,830 --> 00:05:03,310 So you get one by L is equal to custody. 92 00:05:03,590 --> 00:05:06,680 Now we know the value of course that is equal to rule three by two. 93 00:05:06,830 --> 00:05:13,460 So that gives us room three by two is equal to one by equal or you get the value of us two by three. 94 00:05:13,460 --> 00:05:15,440 And that is the answer to this question.