Question

In the adjoining figure, C is the centre of the circle, seg QT is a diameter, CT = 13, CP = 5. Find the length of chord RS.

Answer 1

Given: In a circle with centre C, QT is a diameter, CT = 13 units, CP = 5 units 

To find: Length of chord RS 

Construction: Join points R and C.

i. CR = CT= 13 units …..(i) [Radii of the same circle] 

In ∆CPR, ∠CPR = 90° 

∴ CR² = CP² + RP² [Pythagoras theorem] 

∴ 13² = 5² + RP² [From (i)] 

∴ 169 = 25 + RP² [From (i)] 

∴ RP² = 169 – 25 = 144 

∴ RP = √144 [Taking square root on both sides] 

∴ RP = 12 cm ….(ii)

ii. Now, seg CP _L chord RS [Given] 

∴ RP = (1/2) RS [Perpendicular drawn from the centre of the circle to the chord bisects the chord.] 

∴ 12 = (1/2) RS [From (ii)] 

∴ RS = 2 x 12 = 24 

∴ The length of chord RS is 24 units.