# Geometry (immediate help and explanation)

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A bridge is the shape of an arc of a circle. The bridge is 8 feet tall and 36 feet wide. What is the radius of the circle that contains the bridge? Round your answer to the nearest tenth.

• Geometry (immediate help and explanation) -

Assuming that the 36 feet wide line base is NOT a diameter, make a sketch
let the radius be x
then I see a right-angled triangle where
(x-8)^2 + 18^2 = x^2
x^2 - 16x + 64 + 324 = x^2
-16x = -388
x = 24.25

• Geometry (immediate help and explanation) -

Thanks! But one question..um, where did you get the triangle?

• Geometry (immediate help and explanation) -

draw a whole circle

draw a chord AB, your base , = 36
From the centre O draw a line OA , a radius
let the radius be x
so OA = x, the hypotenuse

from the centre draw a perpendicular to AB to hit AB at C
from C to the circle is 8 , so OC = x-8
OCA is a right - angled triangle.
so ...
see above

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