Question

There are 3 semi circles which are arranged in such a manner that it forms a triangle, as shown in the figure below. If the radius of semicircle A is 4 cm and the radius of semicircle B is 7.5 cm, then find the radius of the semicircle C.

• A. 7.5 cm
• B. 8.5 cm
• C. 17 cm
• D. 15 cm

Answer 1

The correct option is B

8.5 cm

The diameter of a semicircle is given by 2R, i.e. twice the radius of the semicircle. Thus the side XY becomes 2 R i.e, 4 cm + 4 cm = 8 cm and the side YZ becomes 7.5 cm + 7.5 cm = 15 cm. Thus, in triangle XYZ, side XY is 8 cm and side YZ is 15 cm.
Using Pythagoras theorem, we get:

$X{Y}^2+Y{Z}^2=X{Z}^2{\left(8cm\right)}^2+{\left(15cm\right)}^2=X{Z}^{2}64c{m}^2+225c{m}^2=289c{m}^{2}Now,X{Z}^2=289c{m}^{2}XZ=\sqrt{289}c{m}^{2}Thus,sideXZis17cm$
As diameter of a semicircle is given by 2R, so radius is $\frac{17}{2}$ cm = 8.5 cm.