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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

The figure shows a circle with center P and inscribed isosceles Triangle ABC. If AC-example-1
User Shaunlim
by
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2 Answers

3 votes

Answer: 30

it is because I got it right

User Bagle
by
8.3k points
1 vote

Answer:

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

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 =
180^(0)

So that each interior angle =
(180^(0) )/(3)

=
60^(0)

The value of each interior angle of the triangle is
60^(0). Thus, <APC =
60^(0).

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

User Hgminh
by
7.7k points

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