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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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| Photo by Math Principles in Everyday Life |
The area of ∆ABC is
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| 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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| Photo by Math Principles in Everyday Life |
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.
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| 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
