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Question

State true or false for the following statement:

If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, then the chords are equal.

A

True

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B

False

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Solution

The correct option is A. True


Let AB and CD be two chords intersecting at E.

PQ is the diameter passing through E.

AB and CD make equal angles with diameter PQ.

AEQ=DEQ

Draw OLAB and OMCD

In OLE and OME,

OLE=OME=90

OEL=OEM (Given AEQ=DEQ)

OE=OE (common)

OLEOME (By AAS congruence rule)

So, OL=OM (CPCT)

Chord AB and CD are equidistant from the centre.

Hence, AB=CD (Chords equidistant from the centre are equal in length)

Hence the given statement is true.


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