1 00:00:00,520 --> 00:00:05,270 Let's do this question, B, X, Y, C is a rectangle. 2 00:00:05,290 --> 00:00:08,920 All right, it is A and B, C are tangents. 3 00:00:09,310 --> 00:00:13,500 These three lines of tangent to the circle or is the center of the circle. 4 00:00:13,510 --> 00:00:14,080 All right. 5 00:00:14,260 --> 00:00:19,510 Diagonals B and C X meet at all angles. 6 00:00:19,510 --> 00:00:24,370 B, AC is equal to 40 degree find angle X or Y. 7 00:00:25,670 --> 00:00:30,500 Pause the video, give it a try, and then let's do it together is a very good question. 8 00:00:31,130 --> 00:00:32,060 All right, we are back. 9 00:00:32,210 --> 00:00:33,650 I hope you have given it a try. 10 00:00:33,830 --> 00:00:34,980 Let's do it together. 11 00:00:35,300 --> 00:00:42,880 Let's join all with B, B, F, C and E right over here. 12 00:00:42,890 --> 00:00:47,980 We join with these points and let's join up with X and Y also. 13 00:00:48,290 --> 00:00:53,740 Now, remember, it's given that X, C and B, why meet at all? 14 00:00:54,110 --> 00:01:00,340 Right, this this Beevor is a straight line and C, X is a straight line and they meet at all. 15 00:01:00,530 --> 00:01:05,180 But we know angle X or Y will be equal to angle B or C, right. 16 00:01:05,330 --> 00:01:06,060 Why is that so. 17 00:01:06,080 --> 00:01:07,880 Because these are vertically. 18 00:01:13,760 --> 00:01:24,560 All right, so over here, you can see that video F and F or E, C, these two are kite's, right? 19 00:01:24,770 --> 00:01:25,340 Why is that? 20 00:01:25,350 --> 00:01:33,320 So let's take, for example, Biery off over here or is equal to or F because both are radiuses of the 21 00:01:33,350 --> 00:01:33,890 circle. 22 00:01:34,130 --> 00:01:34,450 Right. 23 00:01:34,470 --> 00:01:42,110 So what is equal with and really is equal to be because B and B if are tangent to the circle from an 24 00:01:42,110 --> 00:01:43,010 exterior point. 25 00:01:43,170 --> 00:01:49,400 But whenever you don't draw tangents to a circle from an exterior point, they will be of equal length. 26 00:01:49,610 --> 00:01:52,610 We learn more about this in this section on circles. 27 00:01:52,800 --> 00:01:53,190 All right. 28 00:01:53,330 --> 00:01:55,670 So we have two sets of equal sides. 29 00:01:55,820 --> 00:01:57,890 Therefore, beauty or F is a guide. 30 00:01:58,100 --> 00:02:04,520 And similarly, F or E, C is also a kind because all F is equal or and F is equal to see. 31 00:02:04,760 --> 00:02:09,500 Why is F.C. C because the attendance from an exterior point to this circle. 32 00:02:09,770 --> 00:02:10,180 All right. 33 00:02:10,490 --> 00:02:15,010 Now, in a case we know, that long diagonal is an angle bisecting. 34 00:02:15,040 --> 00:02:15,410 Right. 35 00:02:15,410 --> 00:02:21,380 The long diagonal is an angle by sector, therefore in beedi, or if this angle and this angle will 36 00:02:21,380 --> 00:02:21,920 be equal. 37 00:02:22,070 --> 00:02:27,780 Similarly, in F or easy angle, FLC and C E will be equal. 38 00:02:27,980 --> 00:02:31,090 Let me market us X and X and Y and Y. 39 00:02:31,310 --> 00:02:31,780 All right. 40 00:02:32,450 --> 00:02:36,380 Now you can see that 80 or E is also a kite. 41 00:02:36,650 --> 00:02:37,190 Why is that? 42 00:02:37,190 --> 00:02:43,910 So you have it equal to A and you have B or is equal to only deal is equal to only because they are 43 00:02:43,910 --> 00:02:50,080 radiuses and it is equal to a because they are tangent from an external point to a circle they'll be 44 00:02:50,090 --> 00:02:50,570 of equal. 45 00:02:50,870 --> 00:02:51,200 Right. 46 00:02:51,620 --> 00:02:52,040 All right. 47 00:02:52,280 --> 00:02:53,690 Now over here. 48 00:02:55,030 --> 00:03:00,820 Let's mark this as 1990, we know they are 90 degree because 80 and E are tangents. 49 00:03:00,820 --> 00:03:01,960 It's given in the question. 50 00:03:01,960 --> 00:03:02,230 Right. 51 00:03:02,560 --> 00:03:09,790 And tendons form a 90 degree angle when you draw a line from the point of intersection of the tangent 52 00:03:09,790 --> 00:03:11,080 to the center of the circle. 53 00:03:11,380 --> 00:03:11,760 All right. 54 00:03:11,770 --> 00:03:14,260 So this angle is 90, this angle is 90. 55 00:03:14,270 --> 00:03:15,640 That's how we define a tangent. 56 00:03:15,730 --> 00:03:16,060 All right. 57 00:03:16,330 --> 00:03:21,940 So angle to the or it will be equal to 360 minus 90. 58 00:03:21,940 --> 00:03:23,260 Minus 40. 59 00:03:23,260 --> 00:03:23,590 Right. 60 00:03:23,770 --> 00:03:24,550 Why is that so? 61 00:03:24,580 --> 00:03:27,670 Because it is a four sided polygon. 62 00:03:27,910 --> 00:03:31,260 The sum of the internal angles of a quadrilateral is equal to 360. 63 00:03:31,540 --> 00:03:34,600 We know this angle is 90, this is 90 and this is 40. 64 00:03:34,930 --> 00:03:35,290 Right. 65 00:03:35,450 --> 00:03:42,070 So therefore, this angle over here, that's the only has to be 360, minus 90, minus 90, minus 40. 66 00:03:42,280 --> 00:03:44,110 That's equal to 140 degrees. 67 00:03:44,470 --> 00:03:44,910 All right. 68 00:03:45,070 --> 00:03:53,290 So angle B or C, which is X plus Y will be equal to half of angle D.O.C. That's 70 degrees. 69 00:03:53,290 --> 00:04:00,370 Right, because body is equal to two X plus two way and B or C is X plus white. 70 00:04:02,190 --> 00:04:08,280 All right, so we know that X or Y is equal to B or C, right? 71 00:04:08,490 --> 00:04:13,860 Therefore X or Y angle, X or Y also is equal to 70 degrees. 72 00:04:14,070 --> 00:04:15,720 And that is your answer.