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 cm

B. 8 cm

C. 10 cm

D. 12 cm

Answer :

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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