JEE Main · 2018 · 08 Apr 2018 · Offline · Straight Lines

Let the orthocentre and centroid of a triangle be

A (- 3, 5)

and

B (3, 3)

respectively. If

C

is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is :

(A) $\frac{3 5}{2}$
(B) $10$
(C) $210$
(D) $3 \frac{5}{2}$ ✓ Correct

Answer: (D)

Solution

The orthocentre, centroid and circumcentre lie on the Euler line, with the centroid dividing the segment from orthocentre to circumcentre in the ratio

2 : 1

. Using

G = \frac{H + 2 C}{3}

with the orthocentre

H = (- 3, 5)

and centroid

G = (3, 3)

3 (3, 3) = (- 3, 5) + 2 C

gives

2 C = (12, 4)

, so the circumcentre is

C = (6, 2)

. The segment from

H

C

has length

(6 + 3)^{2} + (2 - 5)^{2} = 81 + 9 = 90 = 310

, and the circle on it as diameter has radius half of this,

\frac{3 10}{2} = 3 \frac{5}{2}

JEE Main · 2018 · 08 Apr 2018 · Offline · Single correct option

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