A circle or radius 2cm touches
a circle of radius 10cm
internally. Determine the length of a segment drawn through
the centre or the larger circle to
the smaller circle
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circle with centre B has radius = 2 cm.
circle with centre A has radius = 10 cm.
Both circle touches internally.
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.
brainlyprince007
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