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if two equal chords of a circle intersect within a circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Asked by vismaya 1st February 2017, 5:47 PM
Answered by Expert

begin mathsize 16px style To space prove colon space angle OMA equals angle OMD
Construction colon space Draw space OP perpendicular OQ
Proof colon
In space increment OMP space and space increment OMQ comma
OM space equals space OM space... left parenthesis common space side right parenthesis
OP space equals space OQ... left parenthesis Since space equal space chords space are space equidistant space from space the space centre right parenthesis
angle OPM equals angle OQM equals 90 degree space... left parenthesis Construction right parenthesis
therefore space ΔOMP space approximately equal to space ΔOMQ space.... left parenthesis RHS space congruence space rule right parenthesis space
angle OMP equals angle OMQ
that space is comma space angle OMA equals angle OMD space space..... left parenthesis cpct right parenthesis space
Hence comma space the space line space joining space the space point space of space intersection space to space the space centre space makes space equal space angles space with space the space chords. end style

Answered by Expert 1st February 2017, 6:04 PM
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