Question

Let A (α, –2), B (α, 6) and C(α/4 , -2) be vertices of a ΔABC. If (5,α/4) is the circumcentre of ΔABC, then which of the following is NOT correct about ΔABC:

(A) ares is 24 

(B) perimeter is 25 

(C) circumradius is 5 

(D) inradius is 2

Answer 1

(B) perimeter is 25 

A (α, –2) : B (α, 6) : C(α/4 , -2)

since AC is perpendicular to AB. 

So, ΔABC is right angled at A.

Circumcentre = mid point of BC. = (5α/8 , 2)

∴ 5α/8 = 5 & α/4 = 2

α = 8

Area = 1/2 (6)(8) = 24

Perimeter = 24 

Circumradius = 5

Inradius = Δ/s = 24/12 = 2