Two tangents drawn from P(1,7) to the circle x^2+y^2=25, touch the circle at Q and R respectively. The area of the quadrilateral PQOR is

MHT CET 2024 Mathematics question

Two tangents drawn from to the circle , touch the circle at Q and R respectively. The area of the quadrilateral PQOR is

(A)16 sq.units
(B)36 sq.units
(C)25 sq.unitsCorrect
(D)49 s.q units

Answer: (C)

Solution

The circle has centre and radius . Since , the length of each tangent is . Also and , . So all four sides of PQOR equal 5 and the angle at Q is , which makes

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Question ID VK-092655