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Question

A circle is tangent to the x and y axes in the first quadrant at the points P and Q respectively. BC and AD are parallel tangents to the circle with slope −1. If the points A and B are on the y- axis while C and D are on the x-axis and the area of the quadrilateral ABCD is 900√2 sq. units, then the radius of the circle is

A
10
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B
12
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C
15
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D
20
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Solution

The correct option is C 15 Radius =α, α∈R Centre =(α,α) MN⊥BC, MN⊥AD Equation of MN is y=x Equation of MN in distance form is x−αcos 45=y−αsin 45∘=α ⇒x=α+α√2=y ∴ Coordinates of M is (α+α√2, α+α√2) Similarly, coordinates of N is (α−α√2, α−α√2) x intercept of AD is 2α+√2α x intercept of BC is 2α−√2α Area of trapezium ABCD =12(AD+BC)MN ⇒900√2=12×√2(4α)×2α⇒α=15

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