1 00:00:00,980 --> 00:00:07,790 Students in this video, let's start discussing some of the interesting properties about a circle which 2 00:00:07,790 --> 00:00:09,500 we will be using in questions. 3 00:00:09,780 --> 00:00:10,240 All right. 4 00:00:10,400 --> 00:00:15,390 Well, here I have a code of this circle and say this is the center of this circle. 5 00:00:15,680 --> 00:00:16,150 All right. 6 00:00:16,250 --> 00:00:18,380 Now, let me name the code as a B.. 7 00:00:18,660 --> 00:00:22,290 OK, now let me draw or be over here. 8 00:00:22,550 --> 00:00:28,370 Now, the property says that if OPIS is perpendicular to Ebbie, right. 9 00:00:28,490 --> 00:00:31,730 That means if these two angles are 90 degrees, right. 10 00:00:31,970 --> 00:00:38,330 Then A B will be equal to be that is this distance will be equal to this distance over here. 11 00:00:38,630 --> 00:00:40,180 Now, can you tell me why that is? 12 00:00:40,190 --> 00:00:42,680 So let's quickly think about it. 13 00:00:43,630 --> 00:00:45,490 It's using congruency of triangles. 14 00:00:45,760 --> 00:00:48,850 It's given that opis perpendicular to a right. 15 00:00:49,090 --> 00:00:53,140 But we know that this angle is equal 90 degrees and this angle is equal to 90 degrees. 16 00:00:53,380 --> 00:01:00,100 Now, if you join or and you get over here and over here, if you join, when you get orbit now, all 17 00:01:00,280 --> 00:01:07,630 will be equal to will be because these two are radiuses of the circle right now in Triangle or EPEAT. 18 00:01:09,740 --> 00:01:21,410 And Triangle or BP, you will see that oil is equal to Olby and OPIS is a common sight and this angle 19 00:01:21,410 --> 00:01:24,080 is equal to 90 degrees and this angle is equal to 90 degrees. 20 00:01:24,290 --> 00:01:26,960 But you can see that these two triangles are congruent. 21 00:01:26,960 --> 00:01:29,990 Asper are as congruency, right? 22 00:01:30,500 --> 00:01:37,700 If these two triangles are congruent, then AP will be equal to BP because these are corresponding sides 23 00:01:37,700 --> 00:01:39,590 of two congruent triangles. 24 00:01:39,920 --> 00:01:40,360 All right. 25 00:01:40,430 --> 00:01:41,390 So let me summarize. 26 00:01:41,570 --> 00:01:48,590 If you have a code and from the center, if you drop a perpendicular to the code, then that perpendicular 27 00:01:48,590 --> 00:01:52,280 line is the bisected of the code that is EBP will be equal to. 28 00:01:53,090 --> 00:01:55,130 Now, the converse of this is also true. 29 00:01:55,310 --> 00:02:00,590 That is, if a particular Beeby then or B will be perpendicular to Ebby. 30 00:02:00,980 --> 00:02:02,880 Let me quickly show you why that is so. 31 00:02:03,110 --> 00:02:06,920 So over here we are starting with a particular beebee. 32 00:02:07,100 --> 00:02:09,630 Now again, we have these two triangles over here. 33 00:02:09,890 --> 00:02:13,200 Now, in this triangle, it's given that it is equal to PB. 34 00:02:13,380 --> 00:02:14,540 So this is equal to this. 35 00:02:14,810 --> 00:02:20,470 And we know always equal will be because these are really and OPIS is a common sight. 36 00:02:20,480 --> 00:02:24,160 So Asper assesses concurrency criteria in this case. 37 00:02:24,170 --> 00:02:30,010 We know that triangle or a B is congruently triangle or B B, right. 38 00:02:30,180 --> 00:02:30,620 Why? 39 00:02:30,650 --> 00:02:32,270 It's because of Essence's rule. 40 00:02:32,280 --> 00:02:33,310 We have seen that over here. 41 00:02:33,590 --> 00:02:39,920 Therefore, you know that this angle is equal to this angle and these two former linear pair also that 42 00:02:39,920 --> 00:02:42,550 is this plus this is equal to 180 degree ends. 43 00:02:42,560 --> 00:02:50,120 We can conclude that OPIS perpendicular to EBR or this angle over here, that's angle B and angle OPV 44 00:02:50,120 --> 00:02:52,040 has to be equal to 90 degrees. 45 00:02:52,700 --> 00:02:54,150 All right, let's move on. 46 00:02:54,290 --> 00:02:56,450 So we have learned two interesting things over here. 47 00:02:56,690 --> 00:03:02,180 We have seen that if you have a code and if a perpendicular is dropped to the code, then it will be 48 00:03:02,180 --> 00:03:02,940 equal to Beebe. 49 00:03:03,200 --> 00:03:09,920 We have also seen that if a line is drawn such that a piece equal to be, then OPIS will be perpendicular. 50 00:03:10,720 --> 00:03:13,460 All right, let's continue to over here. 51 00:03:13,480 --> 00:03:16,920 I have taken one more call, let me name it, as ex-wife. 52 00:03:17,380 --> 00:03:22,910 Now the next property says that say you have or On2 ex-wife. 53 00:03:23,200 --> 00:03:30,730 Now, if it is given that OPIS is perpendicular to Ebbe and or are is perpendicular to exwife. 54 00:03:31,120 --> 00:03:31,440 Right. 55 00:03:31,600 --> 00:03:39,460 If this is true, then if Ekso AB is equal to ex-wife, then it will be will be equal to or if AB is 56 00:03:39,460 --> 00:03:44,860 equal to x y then OPIS will be equal to or and the converse is also true. 57 00:03:44,980 --> 00:03:48,830 That is if OPIS is equal to or then AB is equal to x ray. 58 00:03:49,000 --> 00:03:50,280 Let's try to understand that. 59 00:03:50,410 --> 00:03:56,230 What does it mean if you have two courts such that the perpendicular distance from the center to the 60 00:03:56,230 --> 00:03:57,640 courts are equal? 61 00:03:57,640 --> 00:03:57,930 Right. 62 00:03:58,120 --> 00:03:59,370 That's this case over here. 63 00:03:59,560 --> 00:04:01,850 Then the two courts will be of equal length. 64 00:04:02,320 --> 00:04:08,770 Similarly, if you have two courts of equal length, then the distance of the center to those courts 65 00:04:08,770 --> 00:04:10,120 also will be equal. 66 00:04:10,450 --> 00:04:12,610 Now, let's try to understand why this is so. 67 00:04:13,000 --> 00:04:20,550 Now, let's start with assuming that it's given or B and or perpendicular to Abian X Y. 68 00:04:20,590 --> 00:04:20,890 Right. 69 00:04:21,070 --> 00:04:27,280 So based on what we have learned over here, we know that X R will be equal to our way and AP will be 70 00:04:27,280 --> 00:04:29,390 equal to Beebee because these are perpendicular. 71 00:04:29,590 --> 00:04:30,020 All right. 72 00:04:30,220 --> 00:04:35,810 Now, if say it's given that a B is equal to x ray, let's start with this one over here. 73 00:04:35,860 --> 00:04:38,440 This is let me call the three and let this be four. 74 00:04:38,650 --> 00:04:39,010 All right. 75 00:04:39,010 --> 00:04:40,750 Let's start with this third condition. 76 00:04:40,930 --> 00:04:42,950 So it's given that AB is equal to X Y. 77 00:04:43,060 --> 00:04:43,470 All right. 78 00:04:43,660 --> 00:04:47,950 So then we know that B B will be equal to Ottoway, right. 79 00:04:47,950 --> 00:04:50,530 Because this baby is equal to half of AB. 80 00:04:50,680 --> 00:04:55,940 Ottawa is equal to half of X. So if it is equal to sway, Bebe will be equal to our weight. 81 00:04:56,200 --> 00:04:56,610 All right. 82 00:04:56,740 --> 00:05:01,670 Now let's construct all the way over here and let's construct or be over here. 83 00:05:01,690 --> 00:05:06,400 So I have to right angles triangles whose hypotenuse are equal, right. 84 00:05:06,490 --> 00:05:10,030 Because these two are really high and we have a right angle. 85 00:05:10,030 --> 00:05:16,750 And it is given that B is equal to our weight because every X, Y, therefore Asper artist congruency, 86 00:05:16,990 --> 00:05:22,310 these two triangles will be congruent and hence or will be equal to OPIS. 87 00:05:22,570 --> 00:05:25,060 So that's the proof for the third statement. 88 00:05:25,280 --> 00:05:30,180 But you don't need to know the proof, but it helps to retain and solidify your understanding. 89 00:05:30,310 --> 00:05:33,100 At least you should be able to reason it out to yourself. 90 00:05:33,430 --> 00:05:33,820 All right. 91 00:05:33,820 --> 00:05:34,840 What's the next statement? 92 00:05:34,840 --> 00:05:41,080 That statement for over here, if Opie is equal to or said that is the given statement, again, we 93 00:05:41,080 --> 00:05:44,290 can strike these two triangles right now. 94 00:05:44,290 --> 00:05:49,780 If this is given, then we know this side is equal to this side again or will be equal to or B, because 95 00:05:49,780 --> 00:05:51,190 they are really right. 96 00:05:51,370 --> 00:05:54,940 And we know that this angle over here is equal to this angle over here. 97 00:05:55,120 --> 00:06:01,780 Therefore, as per artist congruency criteria, these two triangles are congruent and hence our Y will 98 00:06:01,780 --> 00:06:04,340 be equal to Beeby and because otherwise. 99 00:06:04,450 --> 00:06:05,680 So let me try that over here. 100 00:06:05,830 --> 00:06:12,850 If you get our way is equal to PBH, then two times our weight will be equal to two times Beeby and 101 00:06:13,090 --> 00:06:17,380 two times our way will be equal to X Y two times B will be equal. 102 00:06:18,100 --> 00:06:18,460 Right. 103 00:06:18,790 --> 00:06:20,260 So that's what we have here. 104 00:06:20,530 --> 00:06:21,760 Let me quickly summarize. 105 00:06:22,890 --> 00:06:30,930 We have learned so far these four properties, right, let's make this clean, that we can quickly revise 106 00:06:30,930 --> 00:06:31,860 what we have learned. 107 00:06:32,400 --> 00:06:37,010 All right, so we have learned these four things, but we started with one call. 108 00:06:37,180 --> 00:06:40,410 If you drop a perpendicular to the code, it will bisect the code. 109 00:06:40,420 --> 00:06:41,910 That is a particular Peevey. 110 00:06:42,180 --> 00:06:47,850 The second statement is if you have a line through the center to a code such that it bisects the code, 111 00:06:48,090 --> 00:06:50,770 then that line is perpendicular to the code. 112 00:06:51,060 --> 00:06:51,530 All right. 113 00:06:51,870 --> 00:06:56,250 The third statement that we learned is if you have two codes, you have an x ray. 114 00:06:56,460 --> 00:07:03,750 And if these two are of equal length, then the perpendicular distance of these two codes from the center 115 00:07:03,750 --> 00:07:04,560 will be equal. 116 00:07:04,740 --> 00:07:08,540 That is, if it is equal to x ray or B will be equal to or. 117 00:07:08,880 --> 00:07:14,430 And the fourth statement is that if you have two codes and it's given that the perpendicular distance 118 00:07:14,430 --> 00:07:20,820 from the center to these two codes are equal, then the two codes will be of equal length.