[Figure: a circle with centre P; chords AB and CD intersect at E inside the circle; seg AC and seg BD are drawn (dashed).]Given : Chords AB and CD of a circle with centre P intersect at point E.To prove : AE × EB = CE × EDConstruction : Draw seg AC a…

Q.3 (A)(2)

[Figure: a circle with centre P; chords AB and CD intersect at E inside the circle; seg AC and seg BD are drawn (dashed).]

Given : Chords AB and CD of a circle with centre P intersect at point E.

To prove : AE × EB = CE × ED

Construction : Draw seg AC and seg BD.

Fill in the blanks and complete the proof.

Proof :

In Δ CAE and Δ BDE

∠AEC ≅ ∠DEB ............ ____

____ ≅ ∠BDE (angles inscribed in the same arc)

∴ Δ CAE ~ Δ BDE ............ ____

∴ \(\dfrac{____}{DE} = \dfrac{CE}{____}\) ............ ____

∴ AE × EB = CE × ED.