In the adjoining figure the diameter of the larger circle is 10 cm and the smaller circle touches internally the larger circle at P and passes through O, the center of the larger circle. Chord SP cuts the smaller circle at R and OR is equal to 4 cm. What is the length of the chord SP?

9 cm

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12 cm

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6 cm

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Solution

The correct option is C
6 cm

OP is the diameter of the smaller circle

$∠$ ORP = 90 (Angle subtended by a diameter)

In triangle ORP

${R P}^{2}$ = ${O P}^{2}$ – ${O R}^{2}$

${R P}^{2}$ = $5^{2}$ – $4^{2}$

RP = 3

Similarly, SR = 3

SP = 3 + 3 = 6 cm

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In the adjoining figure the diameter of the larger circle is 10 cm and the smaller circle touches internally the larger circle at P and passes through O, the center of the larger circle. Chord SP cuts the smaller circle at R and OR is equal to 4 cm. What is the length of the chord SP?

The correct option is C 6 cm OP is the diameter of the smaller circle ∠ ORP = 90 (Angle subtended by a diameter) In triangle ORP RP2 = OP2 – OR2 RP2 = 52 – 42 RP = 3 Similarly, SR = 3 SP = 3 + 3 = 6 cm

The correct option is C
6 cm

OP is the diameter of the smaller circle

$∠$ ORP = 90 (Angle subtended by a diameter)

In triangle ORP

${R P}^{2}$ = ${O P}^{2}$ – ${O R}^{2}$

${R P}^{2}$ = $5^{2}$ – $4^{2}$

RP = 3

Similarly, SR = 3

SP = 3 + 3 = 6 cm