Question

PQ and PR are the two chords of a circle of radius r. If the perpendiculars drawn from the
centre of the circle to these chords are of lengths a and b, PQ = 2PR, then prove that:
b2=2/4+3r2/4

Answer 1

Answer: In the figure above, AB and AC are the chords of the circle with center O and radius r.

such that AB = 2AC

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

in the right angled triangle ONA, using pythagoras thm.