Question

Two tangents PQ and PR drawn to the circle x²+y²-2x-4y-20=0 from point P(16,7). If the centre of the circle is C, the area of quadrilateral PQCR is

• A. 75 sq. unit
• B. 73 sq. unit
• C. 72 sq. unit
• D. 74 sq. unit

Hint:

Tangents from external point are equal.

Answer 1

The Correct Option is C

Centre C(1,2), radius r=5. Distance PC=√((16-1)²+(7-2)²)=√(250). Length of tangent: PQ=PR=√(PC²-r²)=√(225)=15 Area of quadrilateral: 2×\frac12× r× PQ =2×\frac12×5×15=72