Mathematics
In the given figure AB and CD are two parallel chords of a circle. If BDE and ACE are straight lines, intersecting at E, prove that Δ AEB is isosceles.
Circles
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Answer
We know that,
Exterior angle of a cyclic quadrilateral is equal to interior opposite angle.
∠EDC = ∠A ….(i)
∠DCE = ∠B ….(ii)
AB ∥ CD
∠EDC = ∠B [Corresponding angles] ……(iii)
∠DCE = ∠A [Corresponding angles] …….(iv)
From (i), (ii), (iii) and (iv) we get :
∴ ∠A = ∠B
BE = AE [Sides opposite to equal angles are equal]
Hence, proved that ΔAEB is isosceles.
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