Prove that the angle made by two equal chords drawn from a point on the circle is bisected by the diameter through that point.

EG and EH are two equal chords drawn from point E.

EF is the diameter of the circle. GF and HF are joined.

Angle between two chords = ∠GEH.

We have to prove that, ∠GEF = ∠HEF.

In ΔGEF and ΔHEF we have,

EG = EH [given in the problem]

EF is the common side.

∠EGF = ∠EHF = 90° [∵ both are angle inscribed in a semi circle]

∴∆GEF≅∆HEF [SAS congruency]

∴ ∠GEF = ∠HEF [similar angles of congruent triangle]