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? Options: A . &nbsp 2 - √ 2 B . &nbsp √ 2 - 1 C . &nbsp 4 - 2 √ 3 D . &nbsp √ 3 - 1

Answer: Option A : A Now, AO=4 & AOX=45 ∘ ⇒ AX = XO = 2 √ 2 Thus, XY= 4 - 2 √ 2 and the radius of the circle = 4 − 2 √ 2 2 = 2 - √ 2

In the following figure, arc AB is a quadrant of the circle with centre at point

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