In a circle with centre O and of radius 13 cm, two parallel chords are drawn on different sides of the centre. If the length of one chord is 10 cm and the distance between the two chords is 17 cm, then find the difference in lengths of the two chords (in cm).

14

BF = \(\frac{1}{2}\)AB = 5 cm

Applying Pythagoras theorem in \(\Delta \)BOF

\( { BF}^{2 } \) + \( { OF}^{2 } \) = \( { BO}^{2 } \)

⇒ \( { OF}^{2 } \) = \( { 13}^{2 } \) - \( { 5}^{2 } \) = \( { 12}^{2 } \)

⇒ OF = 12 cm

⇒ PE = 17 - 12 = 15 cm.

Applying Pythagoras theorem in OED

⇒ \( { ED}^{2 } \) + \( { OE}^{2 } \) = \( { OD}^{2 } \)

⇒ \( { ED}^{2 } \) = \( { 13}^{2 } \) - \( { 5}^{2 } \) = \( { 12}^{2 } \)

⇒ ED = 12 cm

⇒ CD = 2 x 12 = 24 cm

Difference between the length of the chords = 24 - 10 = 14 cm

Therefore, the difference between the length of the chords = 24 - 10 = 14 cm