Question

In the following figure, arc AB is a quadrant of the circle with centre at point O and radius 4 units. Further, OC = OD, OC:OA = 3:4. A circle C is drawn such that it touches the quadrant at the point Y and the mid-point of AB at X. What is the radius(in units) of the circle C?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Now, AO=4 & AOX=45${}^{\circ }$
$\Rightarrow$ AX = XO = 2$\sqrt{2}$
Thus, XY= 4 - 2$\sqrt{2}$ and the radius of the circle = $\frac{4-2\sqrt{2}}{2}$ = 2 - $\sqrt{2}$