### Question 6

SSC-CGL 2020 Mar 4 Shift 2

In a circle, AB and CD are two chords. When they are extended, they meet at a point P outside the circle such that AB = 7cm, BP = 4.2cm and DP = 2.8cm. Find the length of chord CD?

### Solution in Detail

Remember: Secant-Tangent theorem states that if a chord AB is extended to point P outside the circle, and PQ is a tangent, then PQ² = AP x BPby secant tangent theorem for APQ

$\displaystyle PQ^2 = AP \times BP$

$\displaystyle \text{i.e., } = (7 + 4.2) \times 4.2$

$\displaystyle \therefore PQ^2 = 11.2 \times 4.2\text{. . . (1)}$

Similarly, for CPQ,

$\displaystyle PQ^2 = (2.8 + x) \times 2.8\text{. . . (2)}$

Equating (1) and (2)

$\displaystyle (2.8 + x) \times 2.8 = 11.2 \times 4.2$

Solving, $\displaystyle x = 14\text{ cm }\underline{Ans}$

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