Grades 9-10 Video Solutions 2022-2022_9-10

Video Transcription

Question 29. Five circles with centers A, B, C, D, and E are arranged as shown in the diagram. Line segments are drawn to join the centers of adjacent circles.  It is known that AB equals 16 cm, BC equals 14 cm, CD equals 17 cm, DE equals 13 cm, and AE equals 14 cm. Which point is the center of the circle with the largest radius?  First, let's find the total length of all the segments. So we'll do 16 plus 14 plus 17 plus 13 plus 12 and get 74.  Next, we will divide by two. Since this will give us the total value of all five radii of the five circles, 37. With this, we can start finding out each individual radius.  So the radius of A can be calculated by 37 minus segment BC minus segment DE, or 34 minus 14 minus 13, or the radius of A is 10.  Next, we can do the same for radius B, getting 6, radius of C, and we will get 8. Then with radius D, we will get 9. And finally, with radius E, we will get a radius of 4.  So the point with the center of the circle with the largest radius is the radius of A. So the solution is A.

Video Summary

The problem involves five circles with centers labeled A, B, C, D, and E. Given specific distances between these center points, the task is to identify which center corresponds to the circle with the largest radius. By calculating the total length of these segments and dividing by two, a total value for all radii is found as 37. Each circle's radius is then individually determined, with circle at center A having the largest radius of 10. Therefore, the center of the circle with the largest radius is point A.