Question

PQ and PR are two chords of a circle of radius ( r) .if the perpendicular drawn from the center of the circle to these chords are lenghts a and b PQ=2PR, then proove that :
b^2=a^2/4+3/4 r^2

Answer 1

hola there

In the figure above, AB and AC are the chords of the circle with center O and radius r.
such that AB = 2AC.......(1).

and length of the perpendiculars OM and ON are a and b respectively.
since the perpendicular from the center to the chord bisects the chord.

AM = AB/2 and AN = AC/2.........(2)

in the right angled triangle ONA, using pythagoras thm.
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