1 00:00:00,680 --> 00:00:08,870 Let's do this question, the radius of the circle is five centimeter, Ebe is five square root of three 2 00:00:08,870 --> 00:00:09,770 centimeter. 3 00:00:10,250 --> 00:00:17,540 Find AC this side over here if angle B AC is equal to angle A.B.C.. 4 00:00:17,540 --> 00:00:19,100 So these two angles are equal. 5 00:00:19,310 --> 00:00:19,730 All right. 6 00:00:19,730 --> 00:00:22,830 Pause the video, give it a try and then let's do it together. 7 00:00:23,420 --> 00:00:23,870 All right. 8 00:00:23,870 --> 00:00:24,800 Let's do it together. 9 00:00:25,130 --> 00:00:26,940 These two angles are equal, right? 10 00:00:27,110 --> 00:00:30,620 So Triangle ABC is forming an isosceles triangle. 11 00:00:30,890 --> 00:00:33,790 Therefore AC has to be equal to B.C.. 12 00:00:34,200 --> 00:00:34,600 All right. 13 00:00:34,730 --> 00:00:37,570 Now let's join it to all and be two. 14 00:00:37,570 --> 00:00:46,730 OK, now or A and or B are radiuses therefore or HCB is a quite right because always equal will be and 15 00:00:46,730 --> 00:00:48,230 AC is equal to c.B. 16 00:00:48,230 --> 00:00:54,350 So we have two sets of adjacent sides being equal and OCB is a kite already. 17 00:00:55,760 --> 00:01:02,570 Now let's join up and see, all right, now we know that a the bigger diagonal is the perpendicular 18 00:01:02,570 --> 00:01:04,910 by sector of the shorter one. 19 00:01:05,330 --> 00:01:08,450 Now, let me right the point of intersection aspy. 20 00:01:08,810 --> 00:01:16,280 And in that case, we know AP is equal to B B and this angle over here, angle opihi will be equal to 21 00:01:16,280 --> 00:01:17,230 90 degrees. 22 00:01:17,570 --> 00:01:17,990 All right. 23 00:01:18,230 --> 00:01:21,250 Now we know that the radius of the circle is five centimeter. 24 00:01:21,410 --> 00:01:24,320 So all is equal to or be is equal to five centimeter. 25 00:01:24,650 --> 00:01:29,120 Now we can find PBS Birute three divided by two. 26 00:01:29,240 --> 00:01:29,440 Right. 27 00:01:29,540 --> 00:01:38,660 B, B and B will be five to three by two because the longer diagonal is a big factor of the shorter 28 00:01:38,660 --> 00:01:38,910 one. 29 00:01:38,930 --> 00:01:41,270 So AP IB is the shorter one. 30 00:01:41,450 --> 00:01:45,710 The AP and both of them are equal to fire three by two. 31 00:01:45,950 --> 00:01:51,320 All right, now let's analyze triangle or B B triangle, OPB. 32 00:01:51,320 --> 00:01:53,660 You will see the right angle triangle, right? 33 00:01:54,860 --> 00:02:02,710 Because Angle opened 90 degrees, therefore OPIS Square is equal to Olby Square minus PBIS Square as 34 00:02:02,720 --> 00:02:03,950 per Pythagoras's theorem. 35 00:02:03,950 --> 00:02:09,200 Right, or B is the hypotenuse or B squares or B squared plus B square. 36 00:02:09,410 --> 00:02:13,560 Or you can write or B square is equal to or B squared minus B square. 37 00:02:13,760 --> 00:02:17,470 But that's five square minus Bierut, three by two the whole square. 38 00:02:17,690 --> 00:02:22,950 And hence solving this you will get opis is equal to five divided by two. 39 00:02:23,270 --> 00:02:23,710 All right. 40 00:02:23,870 --> 00:02:27,650 Now let's draw a triangle up over here. 41 00:02:28,830 --> 00:02:35,250 Now, we know this site, OPIS is Fabi two, obvious is five and PB's five by Route three. 42 00:02:35,590 --> 00:02:39,030 Now, let's take a sign of this angle, Teater. 43 00:02:39,180 --> 00:02:42,360 Now more of this you will learn in the section on trigonometry. 44 00:02:42,570 --> 00:02:49,490 Now, SINTA is equal to the ratio of the length of the opposite side to the hypotenuse that is S.T. 45 00:02:49,620 --> 00:02:54,510 in this case is equal to the opposite side of this angle is Beeby. 46 00:02:54,990 --> 00:03:03,570 And the edges inside of the hypotenuse of this triangle is or will be assigned data is equal to be by 47 00:03:03,570 --> 00:03:04,020 Olby. 48 00:03:04,230 --> 00:03:08,160 Now SINTA is five by two or three divided by five. 49 00:03:08,410 --> 00:03:11,010 That's equal to room three by two. 50 00:03:11,950 --> 00:03:19,960 All right, now, when sign data is equal to rule three by two, it will be equal to 60 degree and hence 51 00:03:19,960 --> 00:03:24,370 angle B or B is equal to 60 degrees. 52 00:03:25,270 --> 00:03:33,310 You will see Àngel OCB is equal to anger OBC, these two angles are equal because Albe is equal to Ossy 53 00:03:33,490 --> 00:03:36,190 because Obion OCR radiuses of this circle. 54 00:03:36,190 --> 00:03:40,840 Right now this angle is 60 degrees and these two angles are equal. 55 00:03:41,140 --> 00:03:44,800 Hence these two also have to be equal to 60 degrees. 56 00:03:44,860 --> 00:03:45,210 Right. 57 00:03:45,580 --> 00:03:46,520 That's why. 58 00:03:46,540 --> 00:03:49,390 Why is that so this plus this plus this is 180. 59 00:03:49,570 --> 00:03:57,490 If I said this is X, this is X then 60 plus two X is equal to 180 degree or X is equal to 60 degrees. 60 00:03:57,490 --> 00:03:57,740 Right. 61 00:03:58,000 --> 00:04:01,570 So Triangle OBC is an equilateral triangle. 62 00:04:01,570 --> 00:04:07,870 So Triangle OBC we have found is an equilateral triangle where each angle is equal to sixty degrees. 63 00:04:08,260 --> 00:04:15,250 Now we need to find AC and we have we know that it's easy to see now in this case because triangle obviously 64 00:04:15,250 --> 00:04:16,450 is an equal triangle. 65 00:04:16,600 --> 00:04:20,490 Every side will be equal and we know it will be equal to five centimeter. 66 00:04:20,650 --> 00:04:28,710 Therefore B.C. is also equal to five centimeter and hence AC is equal to five centimeter. 67 00:04:28,870 --> 00:04:30,930 And that is your answer.