Question : A circle with centre O has a chord AB that is 20 cm in length. If the radius of the circle is 12 cm, then the area of triangle AOB is:
Option 1: $20 \sqrt{15}$ cm2
Option 2: $22 \sqrt{11}$ cm2
Option 3: $20 \sqrt{11}$ cm2
Option 4: $22 \sqrt{15}$ cm2
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Correct Answer: $20 \sqrt{11}$ cm2
Solution : The area of triangle AOB, $ = \frac{1}{2} \times \text{base} \times \text{height}$ In triangle AOB, AB is the base and the height is the perpendicular drawn from the centre O to the chord AB. Use the Pythagorean theorem, $OD = \sqrt{12^2 - 10^2} = \sqrt{44} = 2\sqrt{11}$ cm The area of triangle AOB, $\text{Area} = \frac{1}{2} \times AB \times OD = \frac{1}{2} \times 20 \times 2\sqrt{11} = 20\sqrt{11}$ cm2 Hence, the correct answer is $20\sqrt{11}$ cm2.
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Question : A chord of length 40 cm is at a distance of 15 cm from the centre. What is the length of the chord of the same circle which is at a distance of 20 cm from the centre of the circle?
Option 1: 15 cm
Option 2: 25 cm
Option 3: 45 cm
Option 4: 30 cm
Question : In a circle with a centre at O(0,0) and a radius of 5 cm, AB is a chord of length 8 cm. If OM is perpendicular to AB, then the length of OM is:
Option 1: 2.5 cm
Option 2: 3 cm
Option 3: 4 cm
Option 4: 1 cm
Question : The sides of a triangle are of length 8 cm, 15 cm, and 17 cm. Find the area of the triangle.
Option 1: 65 cm2
Option 2: 75 cm2
Option 3: 60 cm2
Option 4: 70 cm2
Question : A chord of length 24 cm is at a distance of 5 cm from the centre of the circle. The radius of the circle is:
Option 1: 13 cm
Option 2: 12 cm
Option 3: 16 cm
Option 4: 15 cm
Question : The distance of a chord OP from the centre of a circle is 6 cm. If the diameter of this circle is 20 cm, then what will be the sum of the radius and length of chord OP?
Option 1: 18 cm
Option 2: 26 cm
Option 4: 20 cm
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