The figure shows a circle with center P and inscribed isosceles Triangle ABC. If AC has the same length as the radius of the cir
cle, what is the measure of angle ABC
1 answer:
Answer:
<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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Step-by-step explanation:
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