Question
In a circle with centre O, ABC is a secant intersecting
the circle at A and B and DC is a tangent to the circle at D. If DC = 12 cm and BC = 6 cm, then the length of AB is equal to:Solution
ATQ,
We have, ⇒ DC = 12 cm and BC = 6 cm ⇒ DC2 = BC × (BC + AB) ⇒ 122 = 6 × (6 + AB) ⇒ 144 = 6 × (6 + AB) ⇒ 144 = 36 + 6AB ⇒ 144 - 36 = 6AB ⇒ 108 = 6AB ⇒ AB = 108 / 6 ⇒ AB = 18 cm ∴ The length of AB is 18 cm.
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