Question

In the given figure, two concentric circles are drawn. If the radius of an inner circle = 3 cm and the length of the chord of an outer circle which touches an inner circle = 8 cm then, find the radius of an outer circle.

• A. 7 cm
• B. 10 cm
• C. 6 cm
• D. 5 cm

Answer 1

Answer: (D)

5 cm

Given - Radius of inner circle = 3 cm and PQ = 8 cm. PQ is the chord of the outer circle which touches the inner circle at L. Join OL and OP.

$\because OL\perp PQ$and OL bisects chord PQ.

$\therefore LP=\frac{1}{2}PQ$

$\therefore LP=\frac{1}{2}\times 8=4cm$
so,
LP = 4 cm and OL = 3 cm (Radius of inner circle)

In right $\Delta$ OLP,

$O{P}^2=O{L}^2+L{P}^2$

$\Rightarrow (OP{)}^2=(3{)}^2+4^2$

$\Rightarrow O{P}^2=9+16$

$\Rightarrow O{P}^2=25$

$\therefore OP=\sqrt{25}=5cm$