Question

Let in a triangle ABC, the line joining orthocentre and circumcentre be parallel to the side BC

 Statement-1 : tan A, tan B, tan C are in A.P.

Statement-2 : If tan A, tan B, tan C are in A.P. then tan A tan C = 3.

(a) Statement-1 is false, Statement-2 is true.

(b) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

(c)  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

(d)  Statement-1 is true, Statement-2 is false.

Answer 1

Correct option  (b) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Explanation:

If tan A, tan B, tan C are in A.P. then

2 tan A = tan A + tan C ⇒ 3 tan B = tan A tan B tan C 

∴ tan B ≠ 0 

⇒ tan A tan C = 3

Now in ΔABC

OH is parallel to BC, so