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If in a triangle P Q R ,sinP ,sinQ ,sinR...

If in a triangle `P Q R ,sinP ,sinQ ,sinRa r einAdotPdot` , then the altitudes are in A.P. the altitudes are in H.P. the medians are in G.P. the medians are in A.P.

A

the altitudes are in AP

B

the altitudes are in HP

C

the altitudes are in GP

D

the altitudes are in AP

Text Solution

Verified by Experts

The correct Answer is:
B
By the law of sine rule,
`(a)/(sinP)=(b)/(sin Q)=(c)/(sinR)=k` [ say]

Also, `(1)/(2)ap_(1)=Delta`
`rArr (2Delta)/(a)=p_(1)`
`rArr p_(1)=(2Delta)/(k sin p)`
Similarly, `p_(2)(2Delta)/(k sin q) and p_(3)=(2Delta)/(k sin R)`
Since sin P sin Q and sin R are in AP, hece, `p_(1)p_(2),p_(3)` are in HP
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