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If in a !ABC , the altitudes from the ve...

If in a `!ABC` , the altitudes from the vertices A , B , C on the opposite sides are in H.P., then sin A, sin B , sin C are in

A

H.P.

B

AGP

C

A.P.

D

G.P.

Text Solution

Verified by Experts

We have,
`Delta=1/2ap_(1)=1/2bp_(2)=1/2cp_(3)`
`rArra=(2Delta)/(p_(1)).b=(2Delta)/(p_(2))` and `c=(2Delta)/(p_(3))`
It JS given that
`p_(1),p_(2),p_(3)` are in H.P.
`rArr1/(p_(1)),1/(p_(2)),1/(p_(3))` are in A.P.
`rArr(2Delta)/(p_(1)),(2Delta)/(p_(2)),(2Delta)/(p_(3))` are in A.P.
`rArr`a, b, c are in A.P.
`rArr` sin A, sin B, sin C are iin A.P.
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OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Section I - Solved Mcqs
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  2. If in a !ABC , sin A, sin B and sin C are in A.P, then

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  3. If in a !ABC , the altitudes from the vertices A , B , C on the opposi...

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  4. In a triangle ABC cos A = 7/8 , cos B = 11/16.then , cos C is equal to

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  5. If the angles A , B , C are the solutions of the equations tan^(3)-3kt...

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  8. Let PQ and RS be tangents at the extremities of the diameter PR of a c...

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  9. If a , b , c denote the sides of a !ABC such that the equation x^(2)+...

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  10. If in a !ABC ,b = 12 units , c = 5 units and != 30 sq. units , then th...

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  11. In a !ABC , 2r = r(1) and A=30 , then cos (B - C)/2 is equal to

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  12. If in a !ABC,a^(2)cos^(2)A=b^(2)+c^(2) , then

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  13. In a triangle ABC , the sides a , b , c are in G.P., then the maximum ...

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  14. The area of a triangle is sqrt3 sq. units and angleB If a^(2),b^(2),c^...

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  15. If in a !ABC , tan A/2 and tan B/2 are the roots of the equation 6x^(2...

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  16. In a !ABC the length of the median AD to the side BC is 4 units. If an...

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  17. Two sides of a triangle are given by the roots of the equation x^(2)-2...

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  18. If in !ABC,(c+a)/b+(c+b)/a=c/r then

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  19. In a !ABC , there is a point D on the side BC such that (BD)/(DC) =1/3...

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  20. If G is the centroid of a DeltaABC, then GA^(2)+GB^(2)+GC^(2) is equal...

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