Question

3. 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 1

Answer:

(C) 10 cm

Explanation:

AB = 12 cm,

BC = 16 cm,

AB ⊥ BC.

Therefore, AC is the diameter of the circle passing through the points A, B and C.

Therefore, AC is the diameter of the circle passing through the points A, B and C. Now, according to the figure, We get,

ABC is a right angled triangle.

ABC is a right angled triangle. 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 LHS and RHS, We get,

Take square root on LHS and RHS, We get, (AC) = 20

Diameter of the circle = 20 cm

Thus, radius of the circle = Diameter/2

= 20/2

= 10 cm

Hence, Radius of the circle = 10 cm

Hence, option C is the correct answer.