In the given figure, there are two concentric circles with centre O.

Question:

In the given figure, there are two concentric circles with centre O. PR and PQS are tangents to the inner circle from point plying on the outer circle. If PR = 7.5 cm, then PS is equal to

(a) 10 cm

(b) 12 cm

(c) 15 cm

(d) 18 cm

Solution:

Let us first draw the radii OSOP and OQ in the given figure, for our convenience.

Consider . We have,

PO = OS (Radii of the same circle)

Therefore, is an isosceles triangle.

We know that in an isosceles triangle, if a line is drawn perpendicular to the base of the triangle from the common vertex of the equal sides, then that line will bisect the base (unequal side).

Therefore, we have

PQ = QS

It is given that,

PQ = 7.5

Therefore,

QS = 7.5

From the figure, we have,

PS = PQ + QS

PS = 7.5 + 7.5

PS = 15

Therefore, option (c) is the correct answer.

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