Angle in a semicircle


Every angle at the circumference subtended by the diameter of a circle is a right angle triangle.

Property 2 can be abbreviated as rt. Ðin a semicircle.







Proof

AôB = 2AĈB ( at centre = 2 at )
But AôB = 180°
AĈB = 90°


Every angle subtended at the circumference by the diameter of a circle is a right angle (90˚).











POQ is the diameter. ∠PAQ = ∠PBQ = ∠PCQ = 90˚.
Example:











O is the centre of the circle. Find the value of x
Solution:
∠ABC = 90˚ ( angle in a semicircle = 90˚)
63˚ + 90˚ + x = 180˚ ( sum of angles in a triangle )
x = 27˚