Question

seg MN is a chord of a circle with centre 0 MN=25, L is a point on chord MN such that ML=9 and distance between O and L is 5 find radius

Answer 1

Draw OP perpendicular to MN (M-L-P-N)
and radius OM.
Let r be the radius of the circle and OP = m.
Now, MP = PN = 12.5
Therefore, LP = 3.5
By Pythagoras theorem,
In triangle MOP
$r ^{2} = m^{2} + 12.5^{2}$

And, in triangle OPL
$5^{2} = m^{2} + 3.5^{2}$
Subtracting first equation from second we get,
r^2 -25 = 144
r^2 = 169
r = 13