Basic Geometric Concepts - Problems on Circles for Exams

Basic Geometric Concepts - Problems on Circles - Case Studies

Q. A circle is inscribed in a triangle with sides 7 cm, 8 cm, and 9 cm. What is the radius of the inscribed circle?

Solution

Semi-perimeter = (7+8+9)/2 = 12 cm. Area = √[12(12-7)(12-8)(12-9)] = √[12*5*4*3] = 12√5. Radius = Area/semi-perimeter = (12√5)/12 = √5 cm.

Correct Answer: B — 3 cm

Q. What is the length of an arc of a circle with a radius of 6 cm and a central angle of 60 degrees?

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2π(6) = 2π cm.

Correct Answer: A — 2π cm

Q. What is the length of an arc of a circle with a radius of 6 cm that subtends an angle of 60 degrees at the center?

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2π(6) = 2π cm.

Correct Answer: A — 2π cm

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