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Question
In the given figure, C is the centre of the circle. seg QT is a diameter CT = 13, CP = 5, find the length of chord RS.
Solution
Draw seg CR
CR = CT = 13 ...(radii of the same circle)
In ΔCPR, ∠CPR = 90°
From Pythagoras' theorem,
CR2 = CP2 + PR2
∴ 132 = 52 + PR2
∴ 169 = 25 + PR2
∴ PR2 = 169 – 25
∴ PR2 = 144
∴ PR = `sqrt(144)`
∴ PR = 12 cm
Now, seg CP ⊥ chord RS
∴ PR = `1/2` RS ...(The perpendicular drawn from the center of the circle to the chord bisects the chord.)
∴ 12 = `1/2` RS
∴ RS = 12 × 2
∴ RS = 24
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