## Thursday, April 24, 2014

### Circle Inscribed - Triangle Problems

Category: Plane Geometry

"Published in Newark, California, USA"

The base of an isosceles triangle is 16 in. and the altitude is 15 in. Find the radius of the inscribed circle.

Solution:

To illustrate the problem, it is better to draw the figure as follows

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The area of ∆ABC is

 Photo by Math Principles in Everyday Life

By using Pythagorean Theorem, we can solve for the two legs of an isosceles triangle as follows

Next, draw the angle bisectors of an isosceles traingle as follows

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The intersection of the angle bisectors of an isosceles triangle is the center of an inscribed circle which is point O. From point O, draw a line which is perpendicular to AB, draw a line which is perpendicular to AC, and draw a line which is perpendicular to BC. These three lines will be the radius of a circle.

 Photo by Math Principles in Everyday Life

The total area of an isosceles triangle is equal to the area of three triangles whose vertex is point O. Therefore, the radius of an inscribed circle is