Let the center of circle C. AB and CD two chords of Length 2a, 2b interest at point P. Let PB = X and PC = y units
Draw Perpendicular OM ⊥ AB
ON ⊥ CD
Join OP = C
Perpendicular from the center bisects the chord
AM = BM = a units
CN = ND = b units
⇒ PM = a - x
PN = b - y
As OMPN is a rectangle and ON = PM = a - x
PN = OM = b - y
From the rectangle OMPN, diagonal
c2 =
(a−x)2+(b−y)2 ......(i)
From the right triangle OAM,
OA2 =
AM2+OM2 r2 =
a2+(b−y)2 .......(ii)
Similarly, right triangle ODN
r2 =
b2+(a−x)2 .......(iii)
Adding (ii) and (iii),
r2+r2 =
a2+b2+(b−y)2+(a−x)2 From (i)
2r2 =
a2+b2+c2 r2 =
r =