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In a triangle PQR " if " angle R =...

In a triangle `PQR " if " angle R = (pi)/(2)` if tan `(P/2)`and `tan (Q/2)` are the roots of ` ax^2 +bx +c=0 , a ne 0` then

A

`a+b=c`

B

`b+c=a`

C

`a+c=b`

D

`b=c`

Text Solution

Verified by Experts

The correct Answer is:
A
It is given that `tan(P//2) and tan (Q//2)` are the roots of the quardratic equations `ax^(2)+bx+c=0`
and `angle R=pi//2`
`:. tan (P//2)+tan(Q//2)=-b//a)`
and `tan(P//2)tan(Q//2)=c//a`
Since, `P+Q+R=180^(@)`
`rArr P+Q=90^(@)`
`rArr (P+Q)/(2)=45^(@)`
`rArr tan ((P+Q)/(2))=tan 45^(@)`
`rArr (tan (P//2)+tan (Q//2))/(1-tan(P//2)tan(Q//2))=1`
`rArr(-b//a)/(1-c//a)=1`
`rArr(-b//a)/((a-c)/(b))=1`
`rArr (-b)/(a-c)=1`
`rArr-b=a-c`
`rArr a+b=c`
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