𝐴, 𝐵, 𝐶 and 𝐷 are points on the circumference of a circle, centre 𝑂.Angle 𝐶𝐴𝐷=28° and 𝐶𝐷=6.4 cm.𝐵𝐷 is a diameter of the circle.Calculate the area of the circle.
Question
𝐴, 𝐵, 𝐶 and 𝐷 are points on the circumference of a circle, centre 𝑂.Angle 𝐶𝐴𝐷=28° and 𝐶𝐷=6.4 cm.𝐵𝐷 is a diameter of the circle.Calculate the area of the circle.
Solution
To solve this problem, we need to find the radius of the circle first. Since BD is the diameter of the circle and CD is a radius, we know that the diameter is twice the length of the radius. Therefore, the radius of the circle is half of 6.4 cm, which is 3.2 cm.
The formula for the area of a circle is πr², where r is the radius of the circle.
Substituting the value of the radius into the formula, we get:
Area = π * (3.2 cm)² = π * 10.24 cm² = 32.17 cm²
So, the area of the circle is approximately 32.17 cm².
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