In this lesson, we will learn
The Thales' theorem states
Every angle subtended at the circumference by the diameter of a circle is a right angle (90˚).
The diameter of a circle always subtends a right angle to any point on the circle.
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.
O is the centre of the circle. Find the value of x
∠ABC = 90˚ ( angle in a semicircle = 90˚)
63˚ + 90˚ + x = 180˚ ( sum of angles in a triangle )
x = 27˚
Inscribed Right Triangles (Right Triangles Inside of Circles)
Thales' Theorem: If the longest side of a triangle inscribed within a circle is the same length as the diameter of a circle, then that triangle is a right triangle, as well as the converse: if a right triangle is inscribed within a circle, the length of its hypotenuse is the diameter of the circle.
We can use the Thales' Theorem to find missing angles.
Proof of the Thales' Theorem
Proof showing that a triangle inscribed in a circle having a diameter as one side is a right triangle.
This proof uses the bow theorem.
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