Question

In the figure, a semicircle with its diameter on the hypotenuse of a right angled triangle, is shown touching the remaining sides of the triangle. The two parts of the hypotenuse made by the centre of the semicircle have lengths 15 cm and 20 cm respectively. Find the radius of the semicircle.

Answer 1

After drawing the figure we can assume that

hypotenuse = AB
And
AC = 15 Cm
BC = 20 Cm

Thus in triangle ABC

AB^2 = AC^2 +  BC^2
 AB^2 = 15^2 + 20^2
          = 225 + 400
AB = 25
Thus Diameter of semicircle = AB = 25 Cm
Thus radius  r = 25/2 = 12.5 Cm