Two concentric circles of radii `3` `cm` and `5` `cm` are given. Then length of chord `BC` which touches the inner circle at `P` is equal to

Options

A. `8` `cm`
B. `9` `cm`
C. `10` `cm`
D. `11` `cm`

Answer

A

Explanation

Let O be the center of the concentric circles

`OP=3 `(radius of smaller circle)

`OB=5`(radius of larger circle)

`/_OPB=/_OPC=90^0` (tangent to the circle is perpendicular to the radius through the point of contact )

And `PC=PB`

Applying Pythagoras theorem in` /_\OPB`

`(OB)^2 = (OP)^2 + (BP)^2`

`:.5^2 = 3^2 + (BP)^2`

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