PQ is a chord of a circle. The tangent XR at X on the circle cuts PQ produced at R. If $X R = 12$ cm, $P Q = x$ cm, $Q R = x - 2$ cm, find $x$ (in cm).

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Solution

The correct option is C $10$
According to the tangent – secant theorem the length of tangent squared equals the product of the secant segment and its external segment

$⟹ P R \times Q R = R X^{2}$

$⟹ (P Q + Q R) \times Q R = X R^{2}$

$⟹ (x + x - 2) (x - 2) = 144$

$⟹ x^{2} - 3 x - 70 = 0$

$(x - 10) (x + 7) = 0$

$x = 10 c m$

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PQ is a chord of a 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, find x (in cm).

The correct option is C 10According to the tangent – secant theorem the length of tangent squared equals the product of the secant segment and its external segment ⟹PR×QR=RX2 ⟹(PQ+QR)×QR=XR2 ⟹(x+x−2)(x−2)=144 ⟹x2−3x–70=0 (x–10)(x+7)=0 x=10cm

PQ is a chord of a circle. The tangent XR at X on the circle cuts PQ produced at R. If $X R = 12$ cm, $P Q = x$ cm, $Q R = x - 2$ cm, find $x$ (in cm).