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In triangle ABC, line joining the cir...

In triangle ABC, line joining the circumcenter and orthocentre is parallel to side AC, then the value of `t a n AtanCi se q u a lto` `sqrt(3)` (b) 3 (c) `3sqrt(3)` (d) none of these

A

`sqrt3`

B

3

C

`3sqrt3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
The distance of circumcenter from side AC is `R cos B`, and the distance of orthocenter from side AC is `2R cos A cos C`. Therefore,
`R cos B = 2R cos A cos C`
`:. Cos (A +C) = 2 cos A cos C`
`:. sin A sin C = 3 cos A cos C`
`:. tan A tan C = 3`
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