1 00:00:00,540 --> 00:00:04,220 Let's do this question, Asaka with Dimitar, SPQR. 2 00:00:04,950 --> 00:00:08,250 All right, is inscribed inside a triangle ABC. 3 00:00:08,280 --> 00:00:14,700 So this is the diameter and you have Triangle ABC and this circle is inscribed inside this triangle. 4 00:00:14,940 --> 00:00:16,980 The circle meets the triangle at R. 5 00:00:16,980 --> 00:00:20,250 S and Z always is the center of the circle. 6 00:00:20,250 --> 00:00:27,930 B is the point of intersection of our Q and B as to argue and P Es are meeting at point B the diameter 7 00:00:27,930 --> 00:00:29,550 of the circle is two centimeter. 8 00:00:29,550 --> 00:00:31,200 Find angle S or R. 9 00:00:31,560 --> 00:00:34,500 S or that's what you need to find out. 10 00:00:34,710 --> 00:00:41,280 If Angle Pudi Q that's b b q this angle is given us two times angle as well. 11 00:00:41,340 --> 00:00:43,820 S who are already was the video. 12 00:00:44,010 --> 00:00:46,110 Give it a try and then let's do it together. 13 00:00:46,900 --> 00:00:47,310 All right. 14 00:00:47,310 --> 00:00:47,760 We are back. 15 00:00:47,760 --> 00:00:48,990 I hope you have given it a try. 16 00:00:49,260 --> 00:00:50,310 Let's do it together. 17 00:00:50,460 --> 00:00:52,560 Let's join up with S and ah. 18 00:00:53,310 --> 00:01:00,890 OK now you can see that these two angles that is all s e and angle or are it will be ninety degree angles. 19 00:01:00,900 --> 00:01:01,250 Right. 20 00:01:01,380 --> 00:01:01,890 Why is that. 21 00:01:01,890 --> 00:01:10,440 So it's mentioned that this circle is inscribed inside this triangle right there for a BBC and AC will 22 00:01:10,440 --> 00:01:12,060 be tangent to the circle. 23 00:01:12,330 --> 00:01:18,930 And we know that if you join the centre to the point of intersection of a tangent and a circle, you 24 00:01:18,930 --> 00:01:20,390 get a ninety degree angle. 25 00:01:20,550 --> 00:01:24,040 So over here you have a ninety degree angle and over here you have it. 26 00:01:24,090 --> 00:01:25,140 Ninety degree angle. 27 00:01:25,320 --> 00:01:29,370 Remember this circle over here is the inner circle of this triangle. 28 00:01:29,460 --> 00:01:29,790 Right. 29 00:01:29,910 --> 00:01:33,270 And this is the in the center of this triangle. 30 00:01:33,420 --> 00:01:34,230 Let's proceed. 31 00:01:34,920 --> 00:01:35,340 So. 32 00:01:37,630 --> 00:01:45,910 Anchor desk, you will be equal to 90 degree Y will be equal to 90 degree angle to is the same as angle 33 00:01:45,910 --> 00:01:46,590 B skew. 34 00:01:46,630 --> 00:01:48,010 Right, both of them are the same. 35 00:01:48,230 --> 00:01:49,870 You can see that from the diagram. 36 00:01:50,110 --> 00:01:55,120 But these this angle will be 90 degrees because it's the angle sub-standard by a diameter. 37 00:01:55,190 --> 00:01:55,510 Right. 38 00:01:55,770 --> 00:02:01,300 Let me clean this up a little bit, but these two will be equal and hence angled skew will be equal 39 00:02:01,300 --> 00:02:02,230 to 90 degrees. 40 00:02:02,560 --> 00:02:03,000 All right. 41 00:02:03,130 --> 00:02:09,730 Now, whatever angle petechia in, you see that angle B, B, Q, that is this angle over here is an 42 00:02:09,730 --> 00:02:12,230 external angle to triangle SPQR. 43 00:02:12,340 --> 00:02:15,770 Right to be recut is obtained by extending side. 44 00:02:15,810 --> 00:02:16,930 Yes, that's right. 45 00:02:16,930 --> 00:02:18,890 Angle PDU is an external angle. 46 00:02:18,890 --> 00:02:20,650 The triangle is dequeue. 47 00:02:21,010 --> 00:02:26,970 Therefore Angle PD Q is equal to ninety degree plus angle is Kutty. 48 00:02:26,980 --> 00:02:30,340 Right, because this angle over here that's angle D. 49 00:02:30,390 --> 00:02:32,660 Q is ninety degree angle pd. 50 00:02:32,710 --> 00:02:36,550 Q is angle dsu plus angle secuity. 51 00:02:36,700 --> 00:02:42,130 Because there's an external angle and we know that external angle is equal to some of the interior opposite 52 00:02:42,130 --> 00:02:42,550 angles. 53 00:02:42,850 --> 00:02:48,880 And over here we have seen that Vesku is ninety, so I have Sub-Zero ninety degrees over here, so that 54 00:02:48,880 --> 00:02:52,930 is equal to 90 plus angle s or BITOU. 55 00:02:53,110 --> 00:02:59,170 Why is that so angle s or is this angle over here and angle is too deep. 56 00:02:59,320 --> 00:03:00,700 Is this angle over here. 57 00:03:01,420 --> 00:03:03,540 You can see that angle is skewed. 58 00:03:03,760 --> 00:03:07,330 The or askew arc which is the same angle is the angle. 59 00:03:07,330 --> 00:03:14,020 SUB-STANDARD by arc is to that will be half of the measure of the arc, the measure of the arc Odyssey's 60 00:03:14,020 --> 00:03:15,370 are right. 61 00:03:15,520 --> 00:03:20,660 So that's why we have an angle skewed as half of angle as or so. 62 00:03:20,680 --> 00:03:23,020 That's one of the properties that we have discussed before. 63 00:03:23,350 --> 00:03:27,820 So therefore I can write this also as equal to two times. 64 00:03:27,830 --> 00:03:29,170 So why is that? 65 00:03:29,170 --> 00:03:31,300 So this is because it's given over here. 66 00:03:31,450 --> 00:03:35,530 Angle PD Q is two times angle and so it's mentioned over here. 67 00:03:35,860 --> 00:03:37,300 So now I can solve this. 68 00:03:37,390 --> 00:03:44,400 I saw by two over here and I have two times as well over here now solving this I get three by two angles 69 00:03:44,410 --> 00:03:50,410 or is equal to ninety degree or angle is or is equal to sixty degrees. 70 00:03:50,590 --> 00:03:52,690 And that is the solution to this question.