The Thales' theorem states
Every angle subtended at the circumference by the diameter of a circle is a right angle (90˚).
or
The diameter of a circle always subtends a right angle to any point on the circle.
or
The angle inscribed in a semicircle is 90˚.
The following diagram shows the Thales' Theorem: Angles in a semi-circle are 90°. Scroll down the page for more examples and solutions.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˚
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