   Chapter 8.CR, Problem 35CR Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

An isosceles right triangle is inscribed in a circle that has a diameter of 12 in. Find the exact area between one of the legs of the triangle and its corresponding arc.

To determine

To find:

The exact area between one of the legs of the triangle and its corresponding arc.

Explanation

Calculation:

Given:

An isosceles right triangle is inscribed in a circle that has a diameter of 12 in.

The diameter is two times the radius.

Diameter (AB) = 12 in.

Diameter=2r12=2×rr=122r=6

Radius = 6 in.

We know that the triangle only coincides in half of the circle.

Thus, the area of the circle around the triangle is:

A=12πr2=12π(6)2=12π(36)=18π

The area of the circle around the triangle = 18π in2

We know that, the triangle forms a 45-45-90 triangle.

To find height:

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