In a right-angled triangle ABC, the length of leg AB is equal to 21 and BC is equal to 28. The circumference of the center

In a right-angled triangle ABC, the length of leg AB is equal to 21 and BC is equal to 28. The circumference of the center of which lies on the hypotenuse AC touches both legs. Find the R circle.

Let us draw straight lines from the center of the circle to the points of tangency of the circle with the legs and denote these points by D and E. OD perpendicular to AB, and OE perpendicular to AC. ОD = ОЕ and is equal to the radius R of the circle

Consider two right-angled triangles ABC and OBD. These triangles are similar since they have a common angle B, OD parallel to AC.

Then AB / BD = AC / OD.

BD = AB – R.

OD = R.

21 / (21 – R) = 28 / R.

588 – 28 * R = 21 * R.

49 * R = 588.

R = 588/49 = 12 cm.

Answer: The radius of the circle is 12 cm.