The figure shows a circle with center P and inscribed isosceles Triangle ABC. If AC has the same length as the radius of the circle, what is the measure of angle ABC

<ABC = (The central angle of a circle is twice any inscribed angle subtended by the same arc).

Step-by-step explanation:

From the diagram, ABC is an inscribed isosceles triangle. But the radius of the circle equals the length AC.

Join P to A and C to form an equilateral triangle. An equilateral triangle has equal sides and angles. So, the value of each interior angle of the equilateral triangle is;

Sum of angle in a triangle =

So that each interior angle =

                                            =

The value of each interior angle of the triangle is . Thus, <APC = .

⇒ <ABC = (The central angle of a circle is twice any inscribed angle subtended by the same arc.)

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