question_answer

The line segments AB and BC are perpendicular to each other. If AB = 4 cm and BC = 3 cm, then radius of the circle passing through A, B, C will be

A)  3.5 cm

B)  2.0 cm

C)  2.5 cm  

D)  4.5 cm

Correct Answer: C

Solution :

 The centre of the circle passing through A, B and C will be the point of intersection of the perpendicular bisectors PQ and PR of AB and BC respectively. Radius,  \[BP=\sqrt{B{{Q}^{2}}+P{{Q}^{2}}}\]                 \[=\sqrt{{{2}^{2}}+{{1.5}^{2}}}\]                 \[=\sqrt{6.25}\]                 \[=2.5\]