In the given figure, lengths of the chords AB and CD are 12 cm and 18 cm respectively and distance between them is 15 cm. Find the radius of the circle.
Let the radius of the circle be r.
Given, AB = 12 cm, CD = 18 cm and FE = 15 cm
We know that perpendicular to the chord from the centre bisects the chord.
and CE=ED=CD2=9 cm
Let OE be x cm. Then OF=15−x cm.
Applying Pythagoras theorem to △AFO,
⇒r2=62+(15−x)2 ... (i)
Applying Pythagoras theorem to △CEO,
⇒r2=92+x2 ... (ii)
Equating equations (i) and (ii), we get
⇒ Radius, r =√117 cm.