Question

AB is a diameter of the circle C(O, r), and radius OD ⊥ AB. If C is any point on arc DB, find BAD and ∠ACD.

Answer 1

Given:

AB is the diameter.

OD ⟂ AB ⇒ D is the midpoint of AB.

C is any point on arc DB.

To find ∠BAD

Since AB is the diameter, the angle standing on it is a right angle:

∠ADB = 90°

D is the midpoint of AB, so:

AD = BD

Thus, triangle ADB is an isosceles right triangle, so the base angles are equal:

∠BAD = ∠ABD

∠BAD = 45°

To find ∠ACD

C lies on arc DB.

Angles standing on the same chord AD are equal.

∠ACD = ∠BAD

∠ACD = 45°