Question

In a ∆ABC, the equation of the side BC is 2x – y = 3 and its circumcentre and orthocentre are at (2, 4) and (1, 2), respectively.

1.  Circumradius of ∆ABC is

(a)  √(61/5)

(b)   √(51/5)

(c)  √(41/5)

(d)  √(43/5)

2. sinB sinC is equal to

(a)  9/2√61

(b)  9/4√61

(c) 9/√61

(d)  9/3√61

 3. The distance of orthocentre of vertex A is

(a)  1/√5

(b)  6/√5

(c)  3/√5

(d)  2/√5

Answer 1

Correct option (A)(B)(B)

1.  Since P(2, 4) is circumcentre and O(1, 2) is orthocentre, PE ⟂ BC and OD ⟂  BC. Let R be the circumradius of ΔABC. Then

(OP)² = R2(1 – 8 cosA cosB cosC)

Also,

2.

 

3. Distance of orthocentre from vertex A = 2R cosA = 6/√5.