1 00:00:00,580 --> 00:00:06,720 Let's do this question, the sakalys inscribed in Triangle Park, you are always the center of the circle, 2 00:00:07,000 --> 00:00:12,120 given that angle or D is seventy five degree find angle copy. 3 00:00:12,340 --> 00:00:12,760 All right. 4 00:00:12,760 --> 00:00:16,260 Pause the video, give it a try and then let's do it together. 5 00:00:17,050 --> 00:00:17,590 All right. 6 00:00:17,740 --> 00:00:18,790 Let's do it together. 7 00:00:18,910 --> 00:00:19,660 Over here. 8 00:00:19,660 --> 00:00:22,030 The circle is inscribed in Triangle Park. 9 00:00:22,030 --> 00:00:26,830 You are right there for the circle is the inner circle of Triangle Epicure. 10 00:00:27,040 --> 00:00:29,530 We have learned about the inner circle in triangles. 11 00:00:29,530 --> 00:00:34,330 Right there in the center is the point of intersection of the angle by right. 12 00:00:34,510 --> 00:00:40,000 And using that point, you find the entry it is and you can draw an inner circle for a triangle. 13 00:00:40,210 --> 00:00:40,630 All right. 14 00:00:40,810 --> 00:00:44,080 Over here, this circle is the inner circle of Triangle Peak. 15 00:00:44,080 --> 00:00:44,920 You you're right. 16 00:00:45,070 --> 00:00:48,700 That means that these angles are equal to 90 degrees. 17 00:00:48,700 --> 00:00:49,030 Right. 18 00:00:49,180 --> 00:00:51,020 But these angles are equal to 90 degrees. 19 00:00:51,070 --> 00:00:51,390 Right. 20 00:00:51,580 --> 00:00:56,890 And peak, you you are A and B are tangents to this circle. 21 00:00:57,160 --> 00:00:57,640 All right. 22 00:00:58,600 --> 00:01:03,130 Let me know that over here, so these three are tangent to the circle. 23 00:01:03,430 --> 00:01:03,910 All right. 24 00:01:03,940 --> 00:01:10,630 Therefore, we know that this distance over here, if I say this is a and let this be D, then Kuai 25 00:01:10,780 --> 00:01:12,340 and Kudi will be equal. 26 00:01:12,340 --> 00:01:12,640 Right. 27 00:01:12,830 --> 00:01:16,450 Because these are tandyn from an exterior point to a circle. 28 00:01:16,660 --> 00:01:19,030 Let me call it of X and X. 29 00:01:19,360 --> 00:01:23,260 Similarly, these two will be equal, so that can be Y Y. 30 00:01:23,530 --> 00:01:25,300 Similarly, these two lines are equal. 31 00:01:25,330 --> 00:01:26,730 So let it be Z NZ. 32 00:01:27,100 --> 00:01:27,550 All right. 33 00:01:28,780 --> 00:01:33,440 Now, we know that the band instruments are from an exterior point are equal. 34 00:01:33,460 --> 00:01:36,490 So that's why we have found that these two are equal. 35 00:01:36,520 --> 00:01:39,250 These two are equal and these two are equal. 36 00:01:39,460 --> 00:01:39,870 All right. 37 00:01:40,000 --> 00:01:47,950 Now, you can notice one more thing over here or A or B and or if these are also of equal length. 38 00:01:47,950 --> 00:01:48,210 Right. 39 00:01:48,220 --> 00:01:53,590 Because these are radii of the inner circle to always equal is equal to or F, right. 40 00:01:53,930 --> 00:01:58,350 Now, let's mark this point as Ian if. 41 00:01:58,360 --> 00:01:59,650 OK, so. 42 00:02:00,950 --> 00:02:07,870 Over here, you can see that D or F, that's me or F ah, this shape over here, right? 43 00:02:08,210 --> 00:02:09,170 This is a kite. 44 00:02:09,440 --> 00:02:14,510 Remember we learned about kites and the quadrilaterals, but this shape is a kite that we know that 45 00:02:14,510 --> 00:02:21,230 over here the offer is a kite and in a kite the bigger diagonal is the angle bicycle. 46 00:02:21,230 --> 00:02:21,590 Right. 47 00:02:21,800 --> 00:02:29,630 Therefore angle or the will be equal to angle or if that is this angle over here will be equal to this 48 00:02:29,630 --> 00:02:30,590 angle over here. 49 00:02:30,890 --> 00:02:34,850 And it's given that angle or that's this angle over here. 50 00:02:36,190 --> 00:02:38,930 Is equal to seventy five degrees. 51 00:02:38,950 --> 00:02:43,450 All right, so we have these two seventy five degrees now. 52 00:02:44,550 --> 00:02:50,280 Let's mark these angles, this angle one and two and three and angle for you will see that angle. 53 00:02:50,280 --> 00:02:53,880 One is equal to angle two and angle three is equal to angle four. 54 00:02:54,030 --> 00:03:01,950 Why is that so all here Q, E or B is a kite and you always the bigger diagonal to the bigger diagonal 55 00:03:02,070 --> 00:03:04,160 is the angle bisected in a kite. 56 00:03:04,290 --> 00:03:05,250 So that's the angle. 57 00:03:05,250 --> 00:03:10,110 One is equal to angle to similarly B, E or F is also a kite. 58 00:03:10,110 --> 00:03:10,370 Right. 59 00:03:10,530 --> 00:03:15,720 And in the kite the bigger and bigger diagonal is the angle by sector angle three is equal to angle 60 00:03:15,720 --> 00:03:16,040 four. 61 00:03:16,260 --> 00:03:19,040 Now remember, what was the criteria for it to be a kite? 62 00:03:19,320 --> 00:03:22,040 Two sets of a decent side should be equal. 63 00:03:22,050 --> 00:03:31,020 So in all these three cases that is D or F are due east or D and B, E, or if you can see that they 64 00:03:31,020 --> 00:03:39,570 have two sets of adjacent sites as equal, for example, in the or F are different R and if are equal 65 00:03:39,570 --> 00:03:42,890 and all and F are equal because these two are really. 66 00:03:43,200 --> 00:03:43,590 All right. 67 00:03:43,740 --> 00:03:48,570 Now let's add a piece to angle one plus angle two plus angle three plus angle four. 68 00:03:48,570 --> 00:03:51,600 If you add up all of these right, how much will you get. 69 00:03:51,750 --> 00:03:58,200 That would be 360 minus seventy five plus seventy five because well here we know this angle is seventy 70 00:03:58,200 --> 00:03:58,740 five degrees. 71 00:03:58,800 --> 00:03:59,160 Right. 72 00:03:59,670 --> 00:04:01,880 And we know this angle is seventy five degrees. 73 00:04:02,220 --> 00:04:06,090 But if you add all these angles it makes one complete revolution. 74 00:04:06,090 --> 00:04:07,670 So that's a 360 degree. 75 00:04:07,950 --> 00:04:13,620 Now if you just want one plus two plus three plus four, that's 360 minus seventy five plus seventy 76 00:04:13,620 --> 00:04:13,920 five. 77 00:04:14,100 --> 00:04:16,110 That gives you two hundred and ten degrees. 78 00:04:16,110 --> 00:04:16,490 Right. 79 00:04:17,220 --> 00:04:17,720 All right. 80 00:04:17,910 --> 00:04:22,110 Now what is asking the question you need to find angle cupie. 81 00:04:22,260 --> 00:04:23,760 That's cupie. 82 00:04:23,940 --> 00:04:26,340 That's angle two plus angle three. 83 00:04:26,340 --> 00:04:27,600 That is what you need to find. 84 00:04:27,840 --> 00:04:33,420 And you can see that angle two plus angle three is the same as two hundred and ten by two. 85 00:04:33,420 --> 00:04:33,720 Right. 86 00:04:33,900 --> 00:04:37,290 Because angle one plus two plus three plus four is two hundred and ten. 87 00:04:37,470 --> 00:04:41,670 That's what we got over here and we know one and two are equal and three and four equal. 88 00:04:41,820 --> 00:04:47,520 So I can write this as two times angle two plus two times angle three is equal to two hundred and ten. 89 00:04:48,000 --> 00:04:52,530 Therefore angle two plus angle three will be equal to two hundred and ten by two. 90 00:04:52,860 --> 00:04:54,600 That's equal to one zero five degrees. 91 00:04:54,810 --> 00:04:57,540 And that is the answer to this question.