Question

PQ is a chord of circle The tangent XR at X on the circle cuts PQ produced at R If XR = 12 cm, PQ = x cm, QR = x - 2 cm then x in cm is

• A. 6
• B. 7
• C. 10
• D. 14

Answer 1

Answer: (C)

10

RX is a tangent and PQ is a chord of the circle.
Now, $R{X}^2=RQ\times PR$
${12}^2=(x-2)(x+x-2)$
$144=(x-2)(2x-2)$
$144=2x^2-2x-4x+4$
$2x^2-6x-140=0$
$x^2-3x-70=0$
$x^2+7x-10x-70=0$
$(x-10)(x+7)=0$
$x=-7,10$
x cannot be negative. Hence, $x=10$