Question

In Triangle ABC. Line joining the Circum-centre and Ortho-centre is Parallel to side AC, then value of tan A tan C is equal to

• A.
• B. 3
• C.
• D. None of these

Answer 1

The correct option is B

3

Distance of circum-centre from side AC=R cos B and
distance of ortho-centre from side AC=2R cos A cos C
$\Rightarrow$ R cos B=2R cos A.cos C
$\Rightarrow$ -cos(A+C)=2cos A.cos C
$\Rightarrow$ sin A. sin C=3cos A.cos C
$\Rightarrow$ tan A.tan C=3