SOLUTION: Equilateral triangle ABC has sides of 22 cm. A circle of radius 5 cm inside it is tangent to sides AB & AC. Find the distance from the circle's centre to side BC, in cm.

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Question 1204856: Equilateral triangle ABC has sides of 22 cm. A circle of radius 5 cm inside it is tangent to sides AB & AC. Find the distance from the circle's centre to side BC, in cm.
Answer by greenestamps(13209) About Me  (Show Source):
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Let D be the midpoint of side BC. Then the center of the circle O is on AD.

Let E be on side AC such that OE is a radius of the circle.

Triangles AEO and ADC are 30-60-90 right triangles.

With AC = 22, DC = 11 and AD = 11*sqrt(3).

And with OE = 5, AO = 10.

The problem asks for the length of OD, which is AD - AO.

ANSWER: 11*sqrt(3)-10