Question

In the figure, a semicircle with its diameter on the
hypotenuse of a right angled triangle is shown
touching the remaining sides of a triangle. The
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.
(Construction : Join OD and OE)

Answer 1

Step-by-step explanation:

Let the length shown in above diagram be T.

The power of circle T

2

=(15−R)(15+R)

From similar triangles (radius / hypotenuse) of right side right angled

triangle =

R

T

=

20

15

=

4

3

Solving R=12 T=9

Arc length in quarter circle =

2

πR

=

2

π.12

=6π.

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