AB and AC are two chords of a circle of radius r such that AB = 2AC. if p and q are distances of AB and AC from the centre , prove that 4q2 = p2 = 3r2
given: AB and AC are two chords of a circle with center O. such that AB=2AC
p and q are the perpendicular distances of AB and AC from center O. i.e OM=p and ON=q
r is the radius of the circle.
proof: join OA.
OM and ON are perpendicular distances of AB and AC from center O.
AN=AC/2 and AM=AB/2 [perpendicular from center to chord intersect at mid-point of the chord]
in right angled triangle ONA,
in the right angled triangle OMA,
from (1) and (2)
which is the required result.
hope this helps you.