Question

ab and CD are two parallel chords of a circle whose diameter is AC prove that AB equal to CD​

Answer 1

Given :

• Two parallel chords AB and CD of a circle C(O, r) such that AC is a diameter of the circle.

To prove :

• AB = CD

Construction :

• Draw OL ⊥ AB and OML CD.

Proof :

Since AB || CD and OL ⊥ AB and OM ⊥ CD.

Therefore, LOM is a straight line.

Again, AB || CD and AC is a transversal.

=> ∠OAL = ∠OCM [Alternate angles]

In ΔOLA and ΔOMC, we have

=> ∠AOL = ∠COM [Vertically opposite angles]

=> ∠OLA = ∠OMA [Each equal to 90°]

and OA = OC [Radii of same circle]

∴ ΔOLA ≅ ΔOMC [By AAS congruency criteria]

=> AL = CM [By C.P.C.T]

=> 2AL = 2CM

[∴ Perpendicular drawn from the centre of a circle to a chord bisects the chord]

=> AB = CD

Answer 2

ur answer is attached..