Q. 33.9( 10 Votes )

# If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is:A. 6 cmB. 8 cmC. 10 cmD. 12 cm

Given: AB = 12 cm, BC = 16 cm, AB BC.

Therefore, the circle passing through the points A, B and C has AC as its diameter.

So, from the figure, ABC is a right angled trianlge.

By Pythagoras theorem:

(AC)2 = (CB)2 + (AB)2

(AC)2 = (16)2 + (12)2

(AC)2 = 256 + 144

(AC)2 = 400

Take square root on both sides:

(AC) = 20

Diameter of the circle = 20 cm

Thus, radius of the circle = Diameter/2 = 20/2 = 10 cm

Radius of the circle = 10 cm

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