Explanation Given: A right triangle with sides 1 and 1 . An inscribed circle within triangle is shown in figure. Formula used: The Pythagoras theorem states that for a right triangle, sum of square of its base and perpendicular is equal to the square of Hypotenuse. Mathematically it can be shown as, h = p 2 + b 2 Here, h is hypotenuse, p is perpendicular and b is base of the right angle triangle. Calculation: Consider the radius of circle is r . Sides are A B = 1 and A C = 1 . Recall the Pythagorean theorem and write the equation for hypotenuse ( A C ). A C = ( A B ) 2 + ( B C ) 2 . substitute 1 for A B and 1 for B C . A C = ( 1 ) 2 + ( 1 ) 2 = 2 Draw the radial lines from the center of the circle to each of the three sides. Form a square with side r with 90 ° angle of triangle.

6th Edition

ISBN: 9780100802797

Author: Dugopolski

Publisher: YUZU

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Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 1.1, Problem 112E

To determine

To calculate: The exact radius of the inscribed circle.

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Chapter 1.1, Problem 111E

Chapter 1.1, Problem 113E

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The exact radius of the inscribed circle .

Solution Summary: The author explains the Pythagoras theorem, which states that for a right triangle, sum of square of its base and perpendicular is equal to Hypotenuse.

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To calculate: The exact radius of the inscribed circle.

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Chapter 1 Solutions