1. Carefully prove the theorem: The sum of the distances from any interior point P to the sides of an equilateral triangle is equal to the length of the triangle's altitude. Hint: Begin by partitioning AABC into three triangles based on the interior point P. Then express the area of AABC as the sum of the areas of these three internal ones. Conclude that the height of AABC is 1+m+n. n m

1. Carefully prove the theorem: The sum of the distances from any interior point P to the sides of an equilateral triangle is equal to the length of the triangle's altitude. Hint: Begin by partitioning AABC into three triangles based on the interior point P. Then express the area of AABC as the sum of the areas of these three internal ones. Conclude that the height of AABC is 1+m+n. n m

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter6: Circles

Section6.3: Line And Segment Relationships In The Circle

Problem 39E: The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle...

See similar textbooks

Similar questions

The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle of radius length 3 inches. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
Determine whether the statement is true or false. a A right circular cone has exactly two bases. b The lateral area L of a right circular cylinder with radius length r and height h is given by L=2rh.
The center of a circle of radius 2 in. is at a distance of 10 in. from the center of a circle of radius length 3 in. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Compute the base area of a right circular cone that is 15.8 centimeters high and has a volume of 1070 cubic centimeters.
The tin can shown at the right has the indicated dimensions. Estimate the number of square inches of tin required for its construction. HINT: Include the lid and the base in the result.