Question

Explanation on thale theorem

Answer 1

Answer:

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle ∠ABC is a right angle.

Answer 2

Thales's theorem: if AC is a diameter and B is a point on the diameter's circle, then the angle at B is a right angle.

Answer:

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle ∠ABC is a right angle. Thales' theorem is a special case of the inscribed angle theorem, and is mentioned and proved as part of the 31st proposition, in the third book of Euclid's Elements.[1] It is generally attributed to Thales of Miletus, who is said to have offered an ox (probably to the god Apollo) as a sacrifice of thanksgiving for the discovery, but sometimes it is attributed to Pythagoras.

Step-by-step explanation:

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

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 ∠OBA = ∠OAB.

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 180°, we have

{\displaystyle \alpha +\left(\alpha +\beta \right)+\beta =180^{\circ }} \alpha+\left( \alpha + \beta \right) + \beta = 180^\circ

{\displaystyle 2\alpha +2\beta =180^{\circ }} {\displaystyle 2\alpha +2\beta =180^{\circ }}

{\displaystyle 2(\alpha +\beta )=180^{\circ }} {\displaystyle 2(\alpha +\beta )=180^{\circ }}

{\displaystyle \therefore \alpha +\beta =90^{\circ }.} \therefore \alpha + \beta =90^\circ.