Question

Find the radius of the circle in the diagram below if BC is 20 ft and CE is 8 feet with work shown?

Answer 1

Given : a circle of radius r is shown in above where BC = 20 ft and CE = 8 ft.

To find : The radius of the circle.

solution : here BC is a tangent to the circle which touches at B. if we join B to centre (let O) then, ∆BOC is a right angled triangle.

from Pythagoras theorem,

OC² = BO² + BC²

⇒(r + 8)² = r² + 20²

⇒r² + 16r + 64 = r² + 400

⇒16r = 400 - 64 = 336

⇒r = 21

Therefore the radius of the circle is 21 ft.

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