Question

In the figure, semicircles are drawn with the sides of a right triangle as diameter.

Prove that the area of the largest semicircle is the sum of the areas of the smaller ones.

Answer 1

In ΔABC, ∠5 = 90°

According to Pythagoras principle,

AB² + BC² = AC² ………. (1)

Radius of the semicircle with diameter

AB = AB/2

Area of the semicircle with diameter AB

Area of the semicircle with diameter BC

Area of the semicircle with diameter AC

Sum of the areas of the smaller semicircles

= π/8 AC² = Area of the largest semicircle