1 00:00:00,690 --> 00:00:01,860 Let's do this question. 2 00:00:02,310 --> 00:00:11,370 ABC is a triangle or is a point at equal distance that's 10 centimeter from A, B and C and it's in 3 00:00:11,370 --> 00:00:12,620 the plain of ABC. 4 00:00:12,630 --> 00:00:13,110 All right. 5 00:00:13,260 --> 00:00:17,320 Angle A, 60 degree angle B, 60 degree find ABC. 6 00:00:17,630 --> 00:00:21,010 Now, pause the video, give it a try and then let's do it together. 7 00:00:21,420 --> 00:00:21,930 All right. 8 00:00:21,930 --> 00:00:22,890 Let's do it together. 9 00:00:23,190 --> 00:00:23,670 Over here. 10 00:00:23,670 --> 00:00:25,910 You have triangle ABC, right. 11 00:00:26,040 --> 00:00:31,680 And it's mentioned that always a point, which is equidistant from A, B and C now. 12 00:00:31,740 --> 00:00:35,370 Therefore, always the sock'em center of this triangle. 13 00:00:35,380 --> 00:00:35,720 Right. 14 00:00:35,880 --> 00:00:36,300 Why? 15 00:00:36,420 --> 00:00:43,980 Because all is equal to Albie's equal or C so you can draw a circle that touches A, B and C, right. 16 00:00:44,160 --> 00:00:46,180 Therefore or is this Sock'Em Center. 17 00:00:46,400 --> 00:00:46,830 All right. 18 00:00:46,980 --> 00:00:50,550 Now it's given that a 60 degree and B 60 degree. 19 00:00:50,700 --> 00:00:55,650 Therefore Anglesey also will be 60 degrees and that means A.B.C. Triangle. 20 00:00:55,650 --> 00:00:58,380 ABC is an equilateral triangle. 21 00:00:59,810 --> 00:01:03,590 All right, now let me join up to a BNC. 22 00:01:04,750 --> 00:01:08,410 OK, so basically we need to find the side of this equilateral triangle. 23 00:01:08,680 --> 00:01:11,880 All right, now let me draw the circle circle, OK? 24 00:01:12,160 --> 00:01:17,080 Now let me extend it or such that it meets B.C. at point B. 25 00:01:18,470 --> 00:01:23,960 OK, now this point over here will make it right angle with B, C. 26 00:01:25,070 --> 00:01:26,070 Why is that so? 27 00:01:26,300 --> 00:01:31,340 Because in an equilateral triangle, if you remember the median. 28 00:01:33,110 --> 00:01:35,090 The perpendicular biosecure. 29 00:01:36,910 --> 00:01:38,050 The altitude. 30 00:01:40,130 --> 00:01:41,780 And the angle sector. 31 00:01:42,650 --> 00:01:48,090 All are the same line, right to all here AP is the median. 32 00:01:48,370 --> 00:01:55,730 It's also the perpendicular bisected of side B.C. It's also the altitude through Vertex and it is also 33 00:01:55,730 --> 00:01:57,590 the angle by sector of angle. 34 00:01:57,950 --> 00:01:58,310 Right. 35 00:01:58,460 --> 00:01:59,810 So we have already covered that. 36 00:01:59,840 --> 00:02:02,660 So let me assume that you know this and let us proceed. 37 00:02:03,500 --> 00:02:05,100 So what is it that we have done? 38 00:02:05,360 --> 00:02:12,490 We have dropped a perpendicular from all to B C and that's meeting B, C at point B. 39 00:02:12,740 --> 00:02:18,380 Now you can see that angle B all be over here will be equal to Angle S.O.P. 40 00:02:19,100 --> 00:02:20,330 Why will they be equal. 41 00:02:21,580 --> 00:02:26,580 Can you tell me that, Bobby, this angle over here will be equal to this angle over here? 42 00:02:27,010 --> 00:02:36,280 They will be equal because if you take Triangle Bobby, that's triangle B or B and Triangle S.O.P. 43 00:02:37,250 --> 00:02:42,560 You will see that these two are congruent, why you have a right angle over here and you have a right 44 00:02:42,560 --> 00:02:43,200 angle over here. 45 00:02:43,490 --> 00:02:48,800 Now, Olby will be equal to Orsi because they are both radii of this Hachem circle. 46 00:02:48,800 --> 00:02:49,130 Right. 47 00:02:49,280 --> 00:02:51,260 And OPIS is a common sight. 48 00:02:51,260 --> 00:02:51,610 Right. 49 00:02:51,800 --> 00:02:59,090 Therefore, as per artist congruence criteria, these two triangles are congruent and hence angle B 50 00:02:59,090 --> 00:03:00,920 or B is equal to an S.O.P. 51 00:03:01,250 --> 00:03:05,300 Now you can see that that will be equal to 60 degrees. 52 00:03:05,570 --> 00:03:07,220 Let me make some space over here. 53 00:03:11,070 --> 00:03:16,210 All right, now each of these angles will be equal to 60 degrees. 54 00:03:16,470 --> 00:03:17,540 Now, why is that? 55 00:03:17,550 --> 00:03:19,550 These are 60 degrees over here. 56 00:03:19,860 --> 00:03:22,650 Below is the angle by sector of B, right. 57 00:03:22,770 --> 00:03:27,900 Because we have seen that the angle by sector median, but perpendicular by sector and altitude are 58 00:03:27,900 --> 00:03:33,030 all the same line for the equilateral triangle or here and will be a 60 angle. 59 00:03:33,030 --> 00:03:34,860 All BP will be 60 by two. 60 00:03:34,860 --> 00:03:35,840 That's thirty degrees. 61 00:03:35,850 --> 00:03:36,180 Right. 62 00:03:36,330 --> 00:03:38,240 And you have a 90 degree angle over here. 63 00:03:38,430 --> 00:03:42,650 Therefore angle BOPE will be 180 minus 90, minus 30. 64 00:03:42,840 --> 00:03:44,310 That's equal to 60 degree. 65 00:03:44,520 --> 00:03:48,300 Similarly, angle S.O.P will also be equal to 60 degrees. 66 00:03:48,600 --> 00:03:50,370 Now let's take sine 60. 67 00:03:50,700 --> 00:03:56,460 That would be BP divided by B or right in triangle BP. 68 00:03:56,460 --> 00:04:03,030 Or if you take sine 60, that would be BP divided by B, right. 69 00:04:04,020 --> 00:04:12,150 All right, so that's opposite side, divided by hypotenuse, that's triangle B, B, or now sine 60, 70 00:04:12,150 --> 00:04:14,820 we know is equal to rule three, divided by two. 71 00:04:16,530 --> 00:04:23,010 All right, now it's given that the distance of all from the vortex is 10 centimeters to be or will 72 00:04:23,010 --> 00:04:25,260 be equal to 10 centimeters right now. 73 00:04:25,290 --> 00:04:26,480 Therefore, let's solve it. 74 00:04:26,610 --> 00:04:29,970 We get BP divided by 10 is equal to room three by two. 75 00:04:30,180 --> 00:04:33,440 Or you can solve BP's five three. 76 00:04:33,810 --> 00:04:38,010 Now, if option is five to three, Donmar, the answer is five to three. 77 00:04:38,220 --> 00:04:38,540 Right. 78 00:04:38,760 --> 00:04:41,940 Because what is asked, we need to find B, c. 79 00:04:42,930 --> 00:04:47,530 Now, BC is equal to Piru trying to do that's equal to 10 Rotary. 80 00:04:47,730 --> 00:04:48,570 Why is that so? 81 00:04:48,750 --> 00:04:54,060 Because BP and B.C. are corresponding sites of two congruent triangles. 82 00:04:55,160 --> 00:05:01,160 Therefore, B.C. is equal to two times five in the rule three, that's 10 rule three, and that is the 83 00:05:01,160 --> 00:05:02,390 answer to this question.