1 00:00:00,670 --> 00:00:07,900 Let's do this question, a semicircle is inscribed in a triangle, ABC The diameter of the same circle 2 00:00:07,900 --> 00:00:08,860 is on ABC. 3 00:00:09,990 --> 00:00:14,550 The sites, AC and Abbi, are tangents to the semicircle. 4 00:00:15,240 --> 00:00:22,010 Amy is given us 13 centimetre acres equal to four centimetre and KB's equal to 15 centimetre. 5 00:00:22,230 --> 00:00:24,700 Find the radius of the semicircle. 6 00:00:24,930 --> 00:00:25,410 All right. 7 00:00:25,650 --> 00:00:26,570 Was the video. 8 00:00:26,760 --> 00:00:29,070 Give it a try and then let's do it together. 9 00:00:29,790 --> 00:00:30,210 All right. 10 00:00:30,210 --> 00:00:30,700 We're back. 11 00:00:30,870 --> 00:00:31,930 Let's do it together. 12 00:00:32,190 --> 00:00:38,370 Over here, we have Triangle ABC and this same circle is inscribed in Triangle ABC. 13 00:00:38,610 --> 00:00:39,120 All right. 14 00:00:39,420 --> 00:00:46,590 Now let's join this point to the center of the semicircle, as well as this point to the center of the 15 00:00:46,590 --> 00:00:47,380 semicircle. 16 00:00:48,240 --> 00:00:52,350 Let it be P and Q and let the center of the semicircle B point are. 17 00:00:52,770 --> 00:01:00,110 Now, it's mentioned that the sides, AC and Ebbie are the engines to the semicircle right now. 18 00:01:00,120 --> 00:01:05,720 Therefore, A, B and B R will make an angle of 90 degrees. 19 00:01:05,850 --> 00:01:11,160 You can refer more on this when you started the engines under the section Sakalys. 20 00:01:11,460 --> 00:01:18,990 So tangents to a circle will form a 90 degree angle when you join the point of intersection of the tangent 21 00:01:18,990 --> 00:01:21,360 to the circle and the center of the circle. 22 00:01:21,510 --> 00:01:26,560 That's why this angle over here is 90 degrees and this angle over here is 90 degrees. 23 00:01:26,940 --> 00:01:27,420 All right. 24 00:01:27,660 --> 00:01:30,270 Now, aspirin's formula. 25 00:01:30,480 --> 00:01:39,180 We know that the area of Triangle ABC is equal to in the S minus E in the S minus B into S minus C right 26 00:01:39,330 --> 00:01:39,660 now. 27 00:01:39,660 --> 00:01:42,300 It's given that the sides of the triangle are 13. 28 00:01:43,590 --> 00:01:51,540 Or and 15 centimeter, therefore, what's the same perimeter that would be 13 plus four plus 15 by two, 29 00:01:51,720 --> 00:01:54,480 which gives you three by two, which is equal to 16. 30 00:01:54,840 --> 00:01:55,290 All right. 31 00:01:55,500 --> 00:02:02,250 Now, let's substitute this into this formula so you get area is equal to root of 16 into three in the 32 00:02:02,250 --> 00:02:03,430 12 into one. 33 00:02:03,780 --> 00:02:06,600 So that gives you the area as four in the two. 34 00:02:06,720 --> 00:02:09,720 The three, which is equal to twenty four centimeter square. 35 00:02:10,050 --> 00:02:10,490 All right. 36 00:02:10,740 --> 00:02:16,200 Now, let me quickly mark the sides of this triangle so we know it's given 13, four and 15. 37 00:02:16,380 --> 00:02:19,080 But I'm just marking them over here now. 38 00:02:21,260 --> 00:02:30,860 Let's join a to our now you can see that the area of Triangle ABC can also be found by adding the area 39 00:02:30,860 --> 00:02:35,980 of Triangle A, B, R and Triangle E, R, C, right. 40 00:02:36,080 --> 00:02:42,890 So that's right that over here the area is equal to area of Triangle Ebarb plus area of Triangle ARCC, 41 00:02:43,010 --> 00:02:44,810 and we have already found the areas. 42 00:02:44,840 --> 00:02:46,970 Twenty four centimeter square over here. 43 00:02:47,420 --> 00:02:56,270 Now we know that this line that is P R is perpendicular to Ebby, that is P R is the altitude through 44 00:02:56,270 --> 00:03:06,410 point are similarly argue is perpendicular to AC, that is our Q is the altitude through our four triangle 45 00:03:06,410 --> 00:03:13,340 area C therefore I can right the area of about as half in to A, B in the upper right. 46 00:03:13,340 --> 00:03:17,450 Based on the formula, that area is equal to half in the base in the height. 47 00:03:17,720 --> 00:03:25,460 Therefore over here the area is half in the 13 into our similarly over here the area is half Endou or 48 00:03:25,460 --> 00:03:31,700 into R and over here I'm digging out an hour because it's the same, same circle, right. 49 00:03:31,700 --> 00:03:33,570 Radius remains the same. 50 00:03:33,740 --> 00:03:35,300 So we use the same variable. 51 00:03:35,540 --> 00:03:43,100 Therefore, the area of Triangle ABC can also be mentioned as half into 13 into our plus avenue, four 52 00:03:43,100 --> 00:03:43,750 into our. 53 00:03:44,180 --> 00:03:52,640 Now that is equal to off into our into 13 plus four, which gives you are by two in to seventeen and 54 00:03:52,640 --> 00:03:55,990 that is equal to twenty four, which is what we have found over here. 55 00:03:56,270 --> 00:04:04,160 Therefore from this equation you can find that R is equal to forty eight by 17 centimeter. 56 00:04:04,310 --> 00:04:06,260 And that is your answer.