In figure 3.79, 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.

Figure: A is outside the circle; AB is a tangent segment and A–C–D is a secant; E lies on chord CD.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

1 answer

Answer: (1) AD = 18 (2) DC = 10 (3) DE = 5

(1) By the tangent secant segments theorem,

\[AB^2 = AC \times AD\] \[144 = 8 \times AD,\quad AD = 18\]

(2) DC = AD − AC = 18 − 8 = 10.

(3) The perpendicular from the centre to a chord bisects the chord, so

\[DE = \frac{1}{2} DC = 5\]

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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