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Offline Centres

The vertices of a triangle are A(–10, 8) B(14, 8) and C(–10, 26). Let G,I,O,S be the centroid in center orthocenter ,circum center respectively of $∆$ ABC
Column - I Column - I
a. The inradius r is p. 15
b. The circum radius R is q. 12
c. $The area of Δ I G o is$ r. 6
d. $The area of Δ S G I is$ s. 3

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a-q; b-r; c-p; d-s

a-r; b-p; c-r; d-s

a-s; b-q; c-r; d-p

answer is A.

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Detailed Solution

$S = \frac{18 + 24 + 30}{2} = 30$

$Area △ A B C = 216$

a) $r = \frac{Δ}{s} = \frac{216}{36} = 6$

b) $R = \frac{30}{2} = 15, \sin θ triangle ABC is right angled$

c) $I = (- 4, 14); G = (- 2, 14); O = A = (- 10, 8)$ $Δ I G O = 6$

d) $S = (2, 17) \Rightarrow Δ S G I = 3$

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