Question

A circle touches the hypotenuse of a right angled triangle at its middle point and passes through the middle point of the shorter side. If 3 unit and 4 unit be the length of the sides and 'r' be the radius of the circle, then the value of 'r' is -

• A. $\frac{1}{6}$
• B. $\frac{3}{5}$
• C. $\frac{5}{3}$
• D. None of these

Answer 1

The correct option is A $\frac{1}{6}$

Left FBE mid-point

Join E and D \angle E=\angle D=x$[Same side]

$ED||BA$

$BA=2ED$

$2x+b=180°90x+C=90°x=C$

Draw a line perpendicular from F

$ED=2r\cos xAB=2\left(2ED\right)=2\left(2r\cos C\right)x=C\Rightarrow 4=4r\cos C\Rightarrow 1=r\frac{3}{5}r=\frac{5}{3}3r=5valueofr=\frac{5}{3}$