Question

suppose AB and AC are equal chords of a circle and a line at A intersects the chords at D and E.prove that AD=AE​.

Answer 1

Step-by-step explanation:

ANSWER

Given- The two chords AC & BD of a circle intersect at E. arcAPB=arcCQD.

To find out- which of the given options is true.

Solution- We join AB, CD and AD. arcAPB=arcCQD⟹AB=CD.......(i) (because equal arcs of a circle contain equal chords). Now the chord AD subtends ∠ABD=∠ACD to the circumference of the given circle at B & C respectively.

∴∠ABD&∠ACD (because the angles, subtended by a chord of a circle to different points of the circumference of the same circle, are equal)........(ii)

Also ∠AEB=DEC (vertically opposite angles).

∴ The third angles i.e ∠BAE=∠CDE..........(iii)

So from (i), (ii) & (iii) we conclude that ΔAEB≅ΔCED

⟹BE=ECandAE=ED.

Ans- Option C.

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