Question

if two intersecting chords of a circle make equal angles witb diameter of the circle passing through the point of intersection of the chords prove chords ard equal?

Answer 1

heey friend here is your answer

Answer 2

Heya mate,
here is your answer,

In this figure AB and CD are two chords intersect at point P. O is the centre of the circle. XY is the diameter of the circle passes through point P.

Given that ∠OPM = ∠OPN

Let OM⊥AB and ON⊥CD

In ∆OMP and ∆ONP

∠OMP = ∠ONP (Each 90°)

∠OPM = ∠OPN (Given)

OP = OP (Common)

∴ ∆OMP ≅ ∆ONP (AAS congruence criterion)

⇒ OM = ON (C.P.C.T)

 

Since the chords AB and CD are equidistant from the centre of the circle so, the chords AB and CD are equal

∴AB = CD


Hope this helps

if you have any further doubt or want any help you can ask me. i would like to help.

Thank you


#Sneha