Equilateral triangle PBJ is inscribed in a circle as shown. determine the measure of arc PB
2 answers:
Answer:
The measure of arc PB is 120°
Step-by-step explanation:
Given: A equilateral triangle PBJ is inscribed in a circle with centre O as shown in attachment.
PBJ is an equilateral triangle. Equilateral triangle has equal angles and sides.
Measure of each angle equilateral triangle is 60°
Hence, ∠BJP=60°
∠BOP and ∠BJP lie on same arc of circle but ∠BJP make at circumference of circle and ∠BOP make at centre of circle.
∠BOP=2∠BJP (Because the angle which is subtended by an arc at the centre of a circle is double the size of the angle subtended at any point on the circumference)
Thus, ∠BOP=2 x 60 = 120°
Hence, The measure of arc PB is 120°
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