Question 16

In a circle, AB and DC are two chords. When AB and DC are produced, they meet at P. If PC = 5.6 cm, PB = 6.3 cm and AB = 7.7 cm, then the length of CD is:

Solution

By the property,
$$PB \times PA = PC \times PD$$
$$6.3 \times (PB + AB) = 5.6 \times (PC + CD)$$
$$6.3 \times (6.3 + 7.7) = 5.6 \times (5.6 + CD)$$
$$6.3 \times (14) = 5.6 \times (5.6 + CD)$$
$$88.2 = 5.6 \times (5.6 + CD)$$
$$15.75 = (5.6 + CD)$$
CD = 10.15 cm

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