Question

Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are 90° .

Answer 1

It is given that BE is the bisector of ∠B.

∴ ∠ABE =

However, ∠ADE = ∠ABE (Angles in the same segment for chord AE)

⇒ ∠ADE =

Similarly, ∠ACF = ∠ADF = (Angle in the same segment for chord AF)

∠D = ∠ADE + ∠ADF

Similarly, it can be proved that