Geometry For Enjoyment And Challenge
Geometry For Enjoyment And Challenge
91st Edition
ISBN: 9780866099653
Author: Richard Rhoad, George Milauskas, Robert Whipple
Publisher: McDougal Littell
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Chapter 16.6, Problem 4PS
To determine

To find: the height of the triangle form inside the circle having diameter 15 .

Expert Solution & Answer
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Answer to Problem 4PS

  h=8 .

Explanation of Solution

Given:

Two side measure 10 and 12 .

Diameter of the circle is 15 .

Concept used:

Heron’s formula:

  A=12×base×height.

  s is semi perimeter:

  s=perimeter2 .

Inradius= As .

Circumradius= abc4A .

Calculation:

Two side measure 10 and 12 .

Let the third side be c and altitude to this side be h .

Area of the triangle =12ch .

According to the given triangle is inscribed in a circle of diameter 15 .

  circumradius=152=abc4A.10×12×c4×12ch=152.h=8.

Hence, the height h=8 .

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