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  • 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

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

Answers (1)

(C) 10 cm

Solution:

Given: AB = 12 cm, BC = 16 cm and AB is perpendicular to BC

AB \perp BC

We know that every angle inscribed in a semicircle is a right angle.

So AOC is the diameter of this circle with O as centre.

Now, applying Pythagoras theorem

\\(Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}\\ AC^{2} = AB^{2} + BC^{2}\\ AC^{2} = 12^{2} + 16^{2}\\ AC^{2} = 144 + 256\\ AC^{2} = 400\\ AC =\sqrt{400} \\AC = 20 cm

As AC is the diameter, Radius

 =\frac{AC}{2} = \frac{20}{2} = 10 cm

Therefore option (C) is correct.

Posted by

infoexpert24

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