Question

(20 Points)

Answer 1

Given:

In circle P, m∠ADB is 25°.

To find:

The m∠APB.

Solution:

Central angle theorem: According to this theorem, the central angle of an arc is twice of inscribed angle of the same arc.

From the given figure it is clear that the ∠APB is the central angle and ∠ADB is the inscribed angle on the arc AB.

By using the central angle theorem, we get

$m\angle APB=2\times m\angle ADB$

$m\angle APB=2\times (25^\circ)$

$m\angle APB=50^\circ$

Therefore, the correct option is D.