In Fig 8.78 there are two concentric circles

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In figure, there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5 cm, find the length of PS.

Solution

Radius from circle bisect the chord
So, PQ = $\frac{1}{2}$ $\times$ PS
$\Rightarrow$ 5 =$\frac{1}{2}$ PS
$\Rightarrow$ PS = 10 cm

Mathematics

RD Sharma

Standard X

In Fig. 8.78, there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5 cm, find the length of PS.

Given that PR = 5 cm.PR and PQ are the tangents to the inner circle so,PR = PQ = 5 cm                                (Tangents drawn from an external point to the circle are equal)Now draw a perpendicular from the centre O to the tangent PS.PS is the chord of the inner circle. we know that the perpendicular drawnfrom the centre of the circle to the chord bisects the chord. So, PQ = QS = 5 cm

PS = PQ + QS = 5 cm + 5 cm = 10 cm

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

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