Question

In the circle, AB is diameter and seg CD is perpendicular to seg AB. If CD = 4 and DB = 8, find AD.​

Answer 1

Step-by-step explanation:

In ∆OCD and ∆OBD

OC = OB (radius)

CD = BD (common tangent)

OD = OD (common)

→∆OCD ≈ ∆ OBD

→ <COD = <BOD

In ∆AOC

OA = OC (radius)

→ <OCA = < OAC

∆COB =<OCA + <OAC (exterior angle of ∆AOC)

→ <COD + <BOD = <OCA + <OCA

→ <COD + <COD = 2<COD

→ 2<COD = 2 <OCA

→ <COD = <OCA

→ AC || OD (alternate angle)

QED

Hence, Proved!..