Question

(ii) A circle of radius 2 cm with centre B touches a circle of radius 10 cm
internally. Determine the length of a tangent segment AP drawn from the
centre A of the larger circle to the smaller circle.​

Answer 1

Given :-

• circle with centre B has radius = 2 cm.
• circle with centre A has radius = 10 cm.
• Both circle touches internally .

To Find :-

• Determine the length of a tangent segment AP drawn from the centre A of the larger circle to the smaller circle. ?

Solution :-

from image we have :-

• AD = radius of bigger circle = 10cm.
• PB = BD = CB = radius of smaller circle = 2 cm.
• AP = tangent to the smaller circle from the centre of bigger circle A.

we know that,

• A tangent makes an angle of 90° with the radius of a circle .

So,

→ ∠APB = 90° .

Now, in right angled ∆APB,

→ PB = 2 cm.

→ AB = AD - BD = 10 - 2 = 8 cm.

therefore,

→ AB² = AP² + PB² (By pythagoras theorem.)

→ 8² = AP² + 2²

→ AP² = 64 - 4

→ AP² = 60

→ AP = √60

→ AP = 2√15 cm. (Ans.)

Hence, Length of a tangent segment AP is 2√15 cm.

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