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Get Answers to all your Questions
Q : 3 If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.
Answers (1)
Given: two equal chords of a circle intersect within the circle.
To prove: the line joining the point of intersection to the centre makes equal angles with the chords.
i.e. OPM=
OPN
Proof :
Construction: Join OP and draw
In OMP and
ONP,
AP = AP (Common)
OM = ON (Equal chords of a circle are equidistant from the centre)
OMP =
ONP (Both are right-angled)
Thus, OMP
ONP (By RHS rule)
OPM=
OPN (CPCT)
View full answer
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