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In triangle ABC," if " BC=8,angleB=30^(@...

In triangle `ABC," if " BC=8,angleB=30^(@),angleC=45^(@)" and "AD "is altitude to to side "BC.`
Assuming AD as diameter, a circle is drawn which cuts side AB and AC at P and Q respectively then find the value of `(PQ)^(2).`

Text Solution

Verified by Experts

`AD=CsinB`
Applying Sine Law in `DeltaAPQ`)
`(PQ)/(sinA)=ADimpliesPQ=ADsinA`
`PQ=(sinA)(csinB)`
`PQ=2RsinAsinBsinC.`
`PQ=asinBsinC`
`=8xx(1)/(2)xx(1)/(sqrt(2))=(4sqrt(2))/(2)=2sqrt(2)`
`(PQ)^(2)=(2sqrt(2))^(2)=8`
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