Mathematics
In the figure (i) given below, ED and BC are two parallel chords of the circle and ABE, ACD are two st. lines. Prove that AED is an isosceles triangle.
Circles
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Answer
BEDC is a cyclic quadrilateral as all of its vertices lie on the circumference of the circle.
∵ exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.
∠ABC = ∠D ….(i)
From figure, as ED is parallel to BC, ∠ABC and ∠E are corresponding angles,
∴ ∠ABC = ∠E ….(ii)
From (i) and (ii)
∠D = ∠E
In △AED,
∠D = ∠E,
∴ AE = AD. (As sides opposite to equal angles are equal)
Hence, proved that △AED is an isosceles triangle.
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