Question

Prove that the quadrilateral formed if possible by the internal angles bisector of any quadrilateral is cyclic​

Answer 1

Answer:

Let ABCD be a quadrilateral in which the angle bisectors AH, BF, CF & DH of internal ∠A, ∠B, ∠C & ∠D respectively form a quadrilateral EFGH. EFGH is cyclic quadrilateral. Hence,EFGH is a cyclic quadrilateral in which the sum of one pair of opposite angles is 180° i.e.∠ FEH + ∠ FGH = 180°.

Answer 2

Step-by-step explanation:

Answer:

Let ABCD be a quadrilateral in which the angle bisectors AH, BF, CF & DH of internal ∠A, ∠B, ∠C & ∠D respectively form a quadrilateral EFGH. EFGH is cyclic quadrilateral. Hence,EFGH is a cyclic quadrilateral in which the sum of one pair of opposite angles is 180° i.e.∠ FEH + ∠ FGH = 180°.