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