In triangle ABC, line joining the circumcenter and orthocenter is parallel to side AC, then the value of tan A tan C is equal to

Question

In triangle ABC, line joining the circumcenter and orthocenter is parallel to side AC, then the value of tan A tan C is equal to

In triangle ABC, line joining the circumcenter and orthocenter is parallel to side AC, then the value of tan A tan C is equal to
A. `sqrt3`
B. 3
C. `3sqrt3`
D. none of these

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

4 views Answered 2023-02-05 15:29