In the right triangle, an altitude is drawn from the right angle to the hypotenuse. Circles are inscribed within each of the smaller triangles. What is the distance between the centers of these circles?

Guest Dec 25, 2020

#1**+1 **

The hypotenuse = 25

The altitude length is product of the legs /hypotenuse = 15 *20 / 25 = 12

The other leg of the right triangle in the upper left of the figure is 9

So...the area of this triangle = (1/2) (product of the legs) (1/2(9 *12) = 54

And we can find the radius, R, of the inscribed circle as follows

54 = (1/2) ( 9 + 12 + 15) R

54 = 18 R

R = 3

Similarly the larger right triangle is a 12 - 16 - 20 right triangle

Its area = (1/2) (12 * 16) = 96

And we can find the radius, R, of the inscribed circle in this triangle as

96= (1/2) (12 + 16 + 20 ) R

96 = 24 R

R = 4

The distance between the centers = 3 + 4 = 7

INCORRECT>>>>>SEE JUGOSLAV'S ANSWER BELOW....

CPhill Dec 25, 2020