1 00:00:00,610 --> 00:00:06,790 High students in this video, let's continue learning about properties of Sakalys, all right, over 2 00:00:06,790 --> 00:00:11,500 here, I have a circle with Center all, and you can see that a B is an arc. 3 00:00:11,680 --> 00:00:17,150 And this arc is suspending an angle at point B, but that's angle APB. 4 00:00:17,540 --> 00:00:17,970 All right. 5 00:00:18,160 --> 00:00:24,260 Now, an interesting property of Sakalys is that the SUB-STANDARD angle is half the measure of the arc. 6 00:00:24,460 --> 00:00:26,380 Now, what is the measure of ARCHABBEY? 7 00:00:26,590 --> 00:00:27,610 That's the angle. 8 00:00:27,610 --> 00:00:28,530 It will be right. 9 00:00:28,540 --> 00:00:34,090 We have seen before that the measure of an arc is the angle that it's substance at the center of the 10 00:00:34,090 --> 00:00:34,550 circle. 11 00:00:34,690 --> 00:00:38,050 So the measure of Arc AB is angle will be. 12 00:00:38,500 --> 00:00:44,470 And as per this property angle, EPB is equal to half of angle. 13 00:00:44,470 --> 00:00:45,150 It will be. 14 00:00:45,460 --> 00:00:48,010 Now let's try to understand why this is so. 15 00:00:48,950 --> 00:00:53,990 Let me join P to all and extended two point or. 16 00:00:55,410 --> 00:00:58,780 Why do this construction over here that at this point over here? 17 00:00:59,130 --> 00:01:05,030 All right, now, what can you tell me about anger or be this anger over here? 18 00:01:05,340 --> 00:01:15,990 You can see that angle or B is equal to Angle or B, B plus angle or B, B, right. 19 00:01:16,170 --> 00:01:17,190 That's this angle. 20 00:01:17,370 --> 00:01:18,320 Plus this angle. 21 00:01:18,330 --> 00:01:19,120 Why is that so? 22 00:01:19,320 --> 00:01:23,010 Because Angle or B is an exterior angle. 23 00:01:24,970 --> 00:01:27,490 Or Triangle or Bebe. 24 00:01:28,910 --> 00:01:36,470 Right, and we have learned that in triangles, the exterior angle is equal to the sum of the interior, 25 00:01:36,470 --> 00:01:40,910 opposite angles to Orombi is an exterior angle and angle. 26 00:01:40,910 --> 00:01:45,350 OPV and Angle or BP are the interior opposite angles. 27 00:01:45,350 --> 00:01:45,660 Right. 28 00:01:45,860 --> 00:01:47,280 But that's why this is true. 29 00:01:47,450 --> 00:01:51,110 Now, over here you can see that OPIS is equal to Olby. 30 00:01:51,380 --> 00:01:57,000 These two are equal because these two are really irate or Pissarides and Albie's radius. 31 00:01:57,200 --> 00:02:03,410 Therefore OPIS equal to or B and hence Triangle or B is an isosceles triangle. 32 00:02:04,970 --> 00:02:11,000 Therefore, we know that these two angles, that is the angles opposite equal sides are equal in an 33 00:02:11,000 --> 00:02:12,040 isosceles triangle. 34 00:02:12,230 --> 00:02:13,910 So these two will be equal, right. 35 00:02:14,030 --> 00:02:17,390 So let me call it as two times angle or B. 36 00:02:18,940 --> 00:02:26,710 So we have seen that R or B is equal to two times or B, B, similarly, you can see that R or A. 37 00:02:27,710 --> 00:02:33,710 Let me write that over here, or it will be equal to two times and will all be. 38 00:02:35,080 --> 00:02:40,630 With the same logic now, if you add up these two together, if you add up these two together, that 39 00:02:40,630 --> 00:02:43,270 should be equal to adding up these two together. 40 00:02:43,450 --> 00:02:49,630 So if you add up R or B Ainaro, you will get A, B or C, that's this angle over here. 41 00:02:50,030 --> 00:02:50,800 Over here. 42 00:02:50,800 --> 00:02:55,180 By adding it up, you get angle B or it's the same as angle AOB. 43 00:02:55,510 --> 00:03:02,700 And when you add up these two together, right, you get two times angle A, B, B, right. 44 00:03:02,920 --> 00:03:09,520 This plus this gives EPB and over here you have two, over here you have a two that's two times EPB. 45 00:03:09,790 --> 00:03:13,030 So therefore you can see that angle. 46 00:03:13,330 --> 00:03:16,810 It will be divided by two gives angle EPB. 47 00:03:17,010 --> 00:03:18,490 That's what we got over here. 48 00:03:18,730 --> 00:03:22,000 So let's quickly revise the property in a circle. 49 00:03:22,060 --> 00:03:28,390 If you have an arc and the arc is attending an angle over here, therefore this angle that is angle 50 00:03:28,390 --> 00:03:32,470 APB will be half the measure of the arc. 51 00:03:32,470 --> 00:03:33,940 That is half of angle. 52 00:03:33,940 --> 00:03:35,670 It will be all right. 53 00:03:36,370 --> 00:03:38,440 Now, let me make some space over here. 54 00:03:42,710 --> 00:03:51,350 Now, over here, we have taken our job as the main Iraq right now, what would have been the case if 55 00:03:51,350 --> 00:03:53,620 Archabbey was the major Iraq? 56 00:03:54,380 --> 00:03:55,670 Let me draw that over here. 57 00:03:55,770 --> 00:03:57,370 So I have a circle, right? 58 00:03:57,650 --> 00:04:00,670 I have Alawa here and I have B over here. 59 00:04:01,010 --> 00:04:02,690 Now we are taking the meds, Iraq. 60 00:04:02,690 --> 00:04:04,220 So that's this sakova here. 61 00:04:05,950 --> 00:04:06,220 Right. 62 00:04:06,490 --> 00:04:10,650 Let this be the center to the measure of the major arc, is this angle right? 63 00:04:12,370 --> 00:04:19,660 OK, let me call this as to top then, if you take an angle over here, let me make this point a point 64 00:04:19,660 --> 00:04:25,150 B that I join it with, and B, to this angle over here will be half of this. 65 00:04:25,180 --> 00:04:25,960 That's theater. 66 00:04:26,170 --> 00:04:29,110 So you need to take it in the correct order. 67 00:04:29,260 --> 00:04:34,690 If you're taking the arc as the major arc, then you need to take an angle on this side of the major 68 00:04:34,690 --> 00:04:34,900 arc. 69 00:04:34,900 --> 00:04:35,130 Right. 70 00:04:35,350 --> 00:04:39,360 If you're taking as a minor arc, then you need to take an angle on this side. 71 00:04:39,490 --> 00:04:41,170 That's the other side of the arc. 72 00:04:41,170 --> 00:04:41,430 Right. 73 00:04:41,620 --> 00:04:45,620 In that case, if this is the order, then this will be to data. 74 00:04:45,820 --> 00:04:50,440 In this case, if this measure is detailed, then this angle over here will be tighter. 75 00:04:51,070 --> 00:04:53,320 Now, let me tell you one more interesting thing. 76 00:04:53,470 --> 00:04:57,670 If you take this point, Peter's over here and join and Peter's right. 77 00:04:58,260 --> 00:05:00,640 Let me make it a straight line. 78 00:05:02,300 --> 00:05:10,100 All right, now over here, you can see that A, B, B and B, B Rush are all four points on a circle, 79 00:05:10,100 --> 00:05:10,370 right? 80 00:05:10,580 --> 00:05:16,550 Later, we will learn that A, B, B, B dash is actually a cyclic quadrilateral. 81 00:05:18,010 --> 00:05:24,270 We will learn about that and in a cyclical little the some of the opposite angles is equal to 180 degrees. 82 00:05:24,490 --> 00:05:29,810 So this angle teeter over here and this angle will be adding up to 180 degrees. 83 00:05:30,010 --> 00:05:34,540 So if this is the order, then this angle over here will be 180 minus detail. 84 00:05:34,810 --> 00:05:36,530 And what would be the measure over here? 85 00:05:36,790 --> 00:05:40,780 We have learned that this will if this is done, this has to be to deter. 86 00:05:40,900 --> 00:05:45,370 So this measure over here has to be two times 180 minus detA. 87 00:05:45,730 --> 00:05:46,090 Right. 88 00:05:46,360 --> 00:05:49,080 That's 360 minus two data. 89 00:05:49,360 --> 00:05:52,000 And that is also valid with what we have learned. 90 00:05:52,000 --> 00:05:52,310 Right. 91 00:05:52,420 --> 00:05:57,610 If this is Dieter, we have learned that this is true, Dieter, and we know that this is one complete 92 00:05:57,610 --> 00:06:01,610 revolution around a point that's equal to 360 degree. 93 00:06:01,750 --> 00:06:05,950 So if this is true, Dieter, then this measure over here will be 360 minus two. 94 00:06:05,950 --> 00:06:08,410 Dieter And that is what we have got over here. 95 00:06:09,010 --> 00:06:09,450 All right. 96 00:06:09,610 --> 00:06:12,470 Let me quickly summarize the points that we have learned so far. 97 00:06:12,730 --> 00:06:19,140 We have seen that you take an hour and you make a point P over here and you make an angle APB. 98 00:06:19,360 --> 00:06:22,570 Then if this is true, this will be equal to Dieter. 99 00:06:22,810 --> 00:06:24,190 That's our first learning. 100 00:06:24,460 --> 00:06:27,550 The second learning is that we should take the right arc. 101 00:06:27,580 --> 00:06:33,640 So in this case, we are taking Archabbey as the minor arc and hence we had to take a point over here 102 00:06:33,790 --> 00:06:36,850 so that this one is the ratio is maintained right now. 103 00:06:36,850 --> 00:06:40,800 If you are taking the major arc, then you need to take a point over here. 104 00:06:40,960 --> 00:06:44,350 And if you join it together, it will still be a one to two ratio. 105 00:06:44,360 --> 00:06:48,690 That is, if this angle is titta, this measure of the major arc will be to titta. 106 00:06:48,910 --> 00:06:50,440 That's our second learning. 107 00:06:50,770 --> 00:06:51,150 Right. 108 00:06:51,730 --> 00:06:59,170 And we have also seen that if I join A, B, B and B, that it's forming a cyclic quadrilateral. 109 00:06:59,320 --> 00:07:02,040 We will learn more about cyclic Waldron's later. 110 00:07:02,320 --> 00:07:09,670 But in this case, if this is Dieter, then this will be 180 minus Dieter because the angles which are 111 00:07:09,670 --> 00:07:13,380 opposite to each other in a cyclic quadrilateral are supplementary. 112 00:07:13,600 --> 00:07:18,220 And we have seen that this holds over here you get three 60 minus two Titta. 113 00:07:18,340 --> 00:07:20,650 And that is also true in the other way. 114 00:07:20,650 --> 00:07:25,000 If we take this as two to then because this forms one complete revolution. 115 00:07:25,330 --> 00:07:29,710 Therefore also this angle over here has to be 360 minus two to.