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:

    “War is a beastly business, it is true, but one proof we are human is our ability to learn, even from it, how better to exist.”
    —M.F.K. Fisher (1908–1992)

    “When children feel good about themselves, it’s like a snowball rolling downhill. They are continually able to recognize and integrate new proof of their value as they grow and mature.”
    —Stephanie Martson (20th century)

    “The proof of a poet is that his country absorbs him as affectionately as he has absorbed it.”
    —Walt Whitman (1819–1892)