Question

In the given figure, O is the centre of the circle and B is a point of contact. seg OE ⊥ seg AD, AB = 12, AC = 8, find
(1) AD (2) DC (3) DE.

Answer 1

(1)
Using tangent secant segment theorem, we have

AB² = AC × AD

⇒ 12² = 8 × AD

⇒ AD = $\frac{144}{8}$ = 18 units

(2)
DC = AD − AC = 18 − 8 = 10 units

(3)
CD is the chord of the circle with centre O.

Also, OE ⊥ CD (​seg OE ⊥ seg AD)

∴ DE = EC = $\frac{\mathrm{DC}}{2}=\frac{10}{2}$ = 5 units (Perpendicular drawn from the centre of a circle on its chord bisects the chord)