Question

In the diagram below, point D is the center of the circle, and the measure of BC is 50".

D
B
What is the measure of ZACD?
A. 65
B.
40
C.
25
D.
50"

Answer 1

C. 25°

Explanation:

A useful relation for this geometry is "an exterior angle of a triangle is equal to the sum of the remote interior angles." The measure of arc BC is the same as the measure of central angle BDC, which is an exterior angle of triangle ACD.

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Triangle ACD has sides AD and CD that are radii of the circle, so it is an isosceles triangle with angle A ≅ angle C. Exterior angle BDC is the sum of those congruent angles:

∠BDC = ∠CAD +∠ACD

50° = 2×∠ACD

25° = ∠ACD . . . . . . . . divide by 2