Mathematics
In a circle with centre O and diameter AB; angle APB is the angle of semicircle. If PA = PB; find the measure of each angle of triangle APB.
Circles
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Answer
Given, O is center of circle. AB is the diameter of the circle.
⇒ PA = PB (Given)
⇒ ∠PAB = ∠PBA = x (let) [Angles opposite to equal sides of a triangle are always equal]
We know that,
Angle in a semi-circle is a right angle.
⇒ ∠APB = 90°
In ΔAPB, using angle sum property
⇒ ∠PAB + ∠PBA + ∠APB = 180°
⇒ x + x + 90° = 180°
⇒ 2x = 180° - 90°
⇒ 2x = 90°
⇒ x =
⇒ x = 45°
⇒ ∠PAB = ∠PBA = 45°
Hence, all angles of the triangles are 45°, 45° and 90°.
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