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In the given figure, DeltaABC is right-a...

In the given figure, `DeltaABC` is right-angled at `B` such that `BC=6cm` and `AB=8cm`. A circle with centre `O` has been inscribed inside the triangle. `OPbotAB`, `OQbotBC` and `ORbotAC`. If `OP=OQ=OR=xcm` then `x=?`

A

`2cm`

B

`2.5cm`

C

`3cm`

D

`3.5cm`

Text Solution

Verified by Experts

`AC^(2)=AB^(2)+BC^(2)=8^(2)+6^(2)=64+36=100`
`impliesAC=sqrt(100)cm=10cm`.
`CR=CQ=(BC-BQ)=(6-x)cm`.
`AR=AP=(AB-BP)=(8-x)cm`
`AC=(AR+CR)=[(8-x)+(6-x)]cm=(14-2x)cm`
`implies(14-2x)=10implies2x=4impliesx=2cm`.
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