Find the unknown length 'Z' of the following figure when BC = 4 cm, CD = 3 cm, and ED = 13 cm.

8 cm

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9 cm

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10 cm

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4 cm

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Solution

The correct option is A
8 cm

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

$A C \times B C = D C \times E C$
(Z + 4) (4) = $3 \times (13 + 3)$
$(Z + 4) = \frac{3 \times 16}{4}$
Z + 4 = 12
Z = 12 - 4
Z = 8

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