Answer:
<ABC = [tex]30^{0}[/tex] (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 = [tex]180^{0}[/tex]
So that each interior angle = [tex]\frac{180^{0} }{3}[/tex]
= [tex]60^{0}[/tex]
The value of each interior angle of the triangle is [tex]60^{0}[/tex]. Thus, <APC = [tex]60^{0}[/tex].
⇒ <ABC = [tex]30^{0}[/tex] (The central angle of a circle is twice any inscribed angle subtended by the same arc.)
