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P is a point on the altitude of !ABC su...

P is a point on the altitude of `!ABC` such that `angleCBP`= `B/3` ,then A.P.is equal to

A

`2asinC/3`

B

`2bsinA/3`

C

`2csinB/3`

D

`2csinC/3`

Text Solution

Verified by Experts

We have, AD= c sin B.
In `DeltaBDP`, we have
`tanB/3=(PD)/(BD)rArrPD=BDtanB/3=ccosBtanB/3`
`thereforeAD=AP+PD`
`rArrc sin B = AP + c cos B tanB/3`
`rArrAP=csinB-ccosBtanB/3`
`rArrAP=(ccosB/3sinB-ccosBsinB/3)/(cosB/3)`
`rArrAP=(csin(2B)/3)/(cosB/3)rArrAP=2csinB/3`
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