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In the given figure, OP=13 cm, AB=7 cm a...

In the given figure, OP=13 cm, AB=7 cm and BP=9 cm. Find the radius of the circle.

Text Solution

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Draw `OD_|_AB.`
`:." "AD=DB`
(`_|_` drawn from the centre bisects the chord)
`implies" "AD=DB=3.5cm`
and `PD=PB+BD=9+3.5=12.5cm`
In right `triangleODP,` by Pythagoras theorem
`OP^(2)=OD^(2)+PD^(2)`
`implies" "(13)^(2)=OD^(2)+(12.5)^(2)`
`implies" "OD^(2)=(13)^(2)-(12.5)^(2)`
`implies" "OD^(2)=169-156.25=12.75`
Now, in right `triangleODB`
`OB^(2)=OD^(2)+DB^(2)`
`implies" "OB^(2)=12.75+(3.5)^(2)=12.75+12.25=25`
`implies" "OB=sqrt(25)=5cm`
Hence, the radius of the circle is 5 cm.
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