Question

If in triangle ABC, line joining the circumcentre and orthocentre is parallel to side AC, then value of tan A⋅tan C is equal to

(A)  √3

(B)  3

(C)  3√3

(D)  None of these

Answer 1

Correct option  (B) 3

Distance of circumcentre from side AC = R cos B and distance of orthocentre from side AC = 2R cos A⋅cos C. So,

R cos B = 2 R 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