On a common hypotenuse AB two right angled triangles ACB and ADB are drawn such that they lie on the opposite sides. Prove that ∠BAC = ∠BDC.

Question

Philoid · Accepted Answer

Given ACB and ADB are two right angled triangles having common hypotenuse AB.

We have to prove that ∠BAC = ∠BDC.

Construction: Join CD.

Proof:

⇒∠C + ∠D = 90° + 90° = 180°

We know that if opposite angles of a quadrilateral are supplementary, then it is a cyclic quadrilateral.

∴ ADBC is a cyclic quadrilateral.

We know that if two angles are of the same arc, then they are equal.

Here, ∠BAC and ∠BDC are made by the same arc BC.

∴ ∠BAC = ∠BDC

Hence proved