Question

prove that the line joining the midpoint of two equal chords of a circle subtends equal angles with the chord.

Answer 1

In the question, they have given that the chords are equal.

Therefore, let the chords be AB and CD.(refer diagram)

Taking ΔABO and ΔCDO

AB=CD(Given)

OA=OC(Radii)

OB=OD(Radii)

∴ΔABO≅ΔCDO(SSS congruency)

∴∠AOB=∠COD (Corresponding parts of congruent triangles are equal)

Hence proved.