Two chords intersect at a point on a circle and the diameter through this point bisects the angle between the chords. Then the chords have the same length.

True

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False

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Solution

The correct option is A True
In $△ O E B & △ O E C,$ they are congruent (SAS)
Three lines are concurrent at E.
Three vertically opposite angles are same. Let them be p, q, r.
$B E = E C$ $\to (1)$
$△ A E O & D E O$ are congruent too (SAS)
$D E = A E$ $\to (2)$
Total lengths of chord
$A E + E C = D E + E B$ (Same) (From $(1)$ & $(2)$ )
Hence, True.

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