Thales' Theorem - Proof

Proof

We use the following facts: the sum of the angles in a triangle is equal to two right angles (180°) and the base angles of an isosceles triangle are equal.

Provided AC is a diameter, angle at B is constant right (90°).
Figure for the proof.

Since OA = OB = OC, OBA and OBC are isosceles triangles, and by the equality of the base angles of an isosceles triangle, OBC = OCB and BAO = ABO.

Let α = BAO and β = OBC. The three internal angles of the ABC triangle are α, α + β and β. Since the sum of the angles of a triangle is equal to two right angles, we have

then

or simply

Read more about this topic:  Thales' Theorem

Famous quotes containing the word proof:

    “Ah! I have penetrated to those meadows on the morning of many a first spring day, jumping from hummock to hummock, from willow root to willow root, when the wild river valley and the woods were bathed in so pure and bright a light as would have waked the dead, if they had been slumbering in their graves, as some suppose. There needs no stronger proof of immortality. All things must live in such a light. O Death, where was thy sting? O Grave, where was thy victory, then?”
    —Henry David Thoreau (1817–1862)

    “Talk shows are proof that conversation is dead.”
    —Mason Cooley (b. 1927)

    “In the reproof of chance
    Lies the true proof of men.”
    —William Shakespeare (1564–1616)