#3 1. Carefully prove the theorem:The sum of the distances from any interiorpoint P to the sides of an equilateraltriangle is equal to the length of thetriangle's altitude.Hint: Begin by partitioning AABC into threetriangles based on the interior point P. Thenexpress the area of AABC as the sum of theareas of these three internal ones. Concludethat the height of AABC is 1+m+n.Euchd demotangent line is alwe A2. Let D be that point on side BC of AABCsuch that AD is the bisector of ZBAC.Prove that ZADC is half the sum of theinterior angle at B and the exteriorangle at C.(I.e., show that ZADC =in the figure.)B + ε2let E be thebe the3. Given that LN L PR and thatO is the center of the circle PLR, angle.then use a theorem previously of ADFG.discussed in class to prove thatLM = NM.Justify each step in your solution.Ba9OMR

Answered: Image /qna-images/answer/d6e7d448-6c4d-41eb-90b0-03f3d59670ec.jpg

E be the e the 3. Given that LN 1 PR and that O is the center of the circle PLR, then use a theorem previously discussed in class to prove that LM = NM. Justify each step in your solution. DFG. P M N R

E be the e the 3. Given that LN 1 PR and that O is the center of the circle PLR, then use a theorem previously discussed in class to prove that LM = NM. Justify each step in your solution. DFG. P M N R

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...

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Question

100%

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.
Euchd demo
tangent line is alwe A
2. Let D be that point on side BC of AABC
such that AD is the bisector of ZBAC.
Prove that ZADC is half the sum of the
interior angle at B and the exterior
angle at C.
(I.e., show that ZADC =
in the figure.)
B + ε
2
let E be the
be the
3. Given that LN L PR and that
O is the center of the circle PLR, angle.
then use a theorem previously of ADFG.
discussed in class to prove that
LM = NM.
Justify each step in your solution.
B
a
9
O
M
R

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