Question 88

If $$A, B$$ and $$C$$ are three points on a circle, where $$BC$$ is the diameter and $$AC = AB = 5\sqrt{2} cm$$. Find the radius of the circle.

Solution

$$BC$$ is the diameter and $$AC = AB = 5\sqrt{2} cm$$

$$ BC^2 = AB^2 + AC^2 $$

= $$(5\sqrt{2})^2 + (5\sqrt{2})^2 $$

= $$ 25 \times 2 \times 2 $$

= 100

BC = 10 cm , diameter of circle

radius =$$ \frac{10}{2} $$

= 5 cm

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