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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


Team Careers360 17th Jan, 2024
Answer (1)
Team Careers360 19th Jan, 2024

Correct Answer: $20 \sqrt{11}$ cm 2


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,
$\text{Area} = \frac{1}{2} \times AB \times OD = \frac{1}{2} \times 20 \times 2\sqrt{11} = 20\sqrt{11}$ cm 2
Hence, the correct answer is $20\sqrt{11}$ cm 2 .

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