Question

Find the unknown length 'Y' in the given figure.

• A. 32 cm
• B. 16 cm
• C. 8 cm
• D. 24 cm

Answer 1

The correct option is A

32 cm

When 2 chords of a circle intersect internally or externally then the products of the lengths of segments are equal.

i.e. PA x PB = PD x PC
$\Rightarrow 7\times (7+8)=3\times (3+Y)\Rightarrow 7\times \left(15\right)=3\times (3+Y)$
$\Rightarrow 7\times \left(15\right)=3\times (3+Y)$
$\Rightarrow$ 35 = 3 + Y
$\Rightarrow$ 32 = Y
$\therefore$ CD = Y = 32 cm