Q.148. Geometry, Circles touching

Question 148.
Two circles of equal radii are inscribed in a semi circle of radius 1 such that they toucheach other externally.
Find the radii of the inscribed circles.

Answer 148.

Let r = radius of the inscribed circle.

Join the center of the semicircle to the center of the inscribed circle.

From the figure,

r√2 + r = 1
=> r
= 1/(√2 + 1)
= √2 - 1.

Link to YA!