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Q.

The vertices of triangle are , $A (- 10, 8), B (14, 8) C (- 10, 26)$ , Let G, I, O, S be the centroid, Incenter, orthocenter , circumcenter of $Δ A B C$ respectively
List – I List – II
1) Then inradius r is a) 15
2) The circumradius R is b) 12
3) The area of $Δ I G O$ is c) 6
4) The area of $Δ S G I$ is d) 3

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a

$(1) \to c; (2) \to a; (3) \to c; (4) \to d$

b

$(1) \to b; (2) \to c; (3) \to a; (4) \to d$

c

$(1) \to d; (2) \to b; (3) \to c; (4) \to a$

d

$(1) \to d; (2) \to b; (3) \to a; (4) \to c$

answer is A.

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Detailed Solution

$a = B C = 30; b = C A = 18; c = A B = 24$ .
$S = \frac{18 + 24 + 30}{2} = 36; Δ = 216$ .
1) $r = Δ / s = \frac{216}{36} = 6$
2) $R = \frac{30}{2} = 15$
3) $I = (- 4, 14), G (- 2, 14), O = A = (- 10, 8)$
$Δ I G O = 6$
4) $S (2, 17) \Rightarrow Δ S G I = 3$ .

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