If two chords of a circle are equally inclined to the diameter through their point of intersection, prove the chords are equal.

Asked by pereiracalida | 10th Jan, 2018, 06:52: PM

Expert Answer:

 
begin mathsize 16px style According space to space question comma space the space figure space will space be space as space shown space above.
AB space and space AC space are space two space chords space which space are space equally space inclined space to space the space diameter space AD space of space circle space with space
centre space straight O.
Construction colon space Draw space OL perpendicular AB space and space OM perpendicular AC
In space triangles space OLA space and space OMA comma
angle OLA equals angle OMA space space space space space left parenthesis Each space 90 degree right parenthesis
OA equals OA space space space space space left parenthesis common right parenthesis
angle OAL equals angle OAM space space space left parenthesis Given right parenthesis
rightwards double arrow triangle OLA approximately equal to triangle OMA space space space space left parenthesis By space AAS space congruence right parenthesis
rightwards double arrow OL equals OM space space space space left parenthesis CPCT right parenthesis
rightwards double arrow Chords space are space equidstant space from space centre space straight O.
rightwards double arrow AB equals AC end style

Answered by Rashmi Khot | 11th Jan, 2018, 09:38: AM