L A C H B 1 2 Problem. Given two points A, B on the same side of line Find the point C on L such...
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Transcript of L A C H B 1 2 Problem. Given two points A, B on the same side of line Find the point C on L such...
![Page 1: L A C H B 1 2 Problem. Given two points A, B on the same side of line Find the point C on L such that and make congruent angles with L.](https://reader036.fdocuments.net/reader036/viewer/2022082501/5a4d1b717f8b9ab0599b56f0/html5/thumbnails/1.jpg)
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Problem. Given two points A, B on the same side of line Find the point C on L such that and make congruent angles with L .
CA CB
![Page 2: L A C H B 1 2 Problem. Given two points A, B on the same side of line Find the point C on L such that and make congruent angles with L.](https://reader036.fdocuments.net/reader036/viewer/2022082501/5a4d1b717f8b9ab0599b56f0/html5/thumbnails/2.jpg)
Problem. Point Q is called a center of symmetry for figure F if whenever is a segment having Q as midpoint and A in F, then also belongs to F. Show that a figure can only have zero, one, or infinitely many centers
of symmetry .
A
A
O
O
O OL
O O
AA A
![Page 3: L A C H B 1 2 Problem. Given two points A, B on the same side of line Find the point C on L such that and make congruent angles with L.](https://reader036.fdocuments.net/reader036/viewer/2022082501/5a4d1b717f8b9ab0599b56f0/html5/thumbnails/3.jpg)
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1O 2O
3O
1I 2I
3I
Problem. Let L, M, N be the respective midpoints of sides AB, BC, CA of . Let , , be the circumcenters of triangles , , respectively, and let , , be the incenters of these same triangles. Show that
ABC 1O 2O 3OALN BLM CMN
1I 2I 3I.321321 IIIOOO
![Page 4: L A C H B 1 2 Problem. Given two points A, B on the same side of line Find the point C on L such that and make congruent angles with L.](https://reader036.fdocuments.net/reader036/viewer/2022082501/5a4d1b717f8b9ab0599b56f0/html5/thumbnails/4.jpg)
Problem. Given three parallel lines, find an equilateral triangle whose vertices lie on them.
L
M
A
M
M
CB
![Page 5: L A C H B 1 2 Problem. Given two points A, B on the same side of line Find the point C on L such that and make congruent angles with L.](https://reader036.fdocuments.net/reader036/viewer/2022082501/5a4d1b717f8b9ab0599b56f0/html5/thumbnails/5.jpg)
Problem. For any triangle , construct equilateral triangles on the sides of , exterior to it. Show that the centers of these triangles also form the vertices of an
equilateral triangle .
A
B C
1O
2O
3O3OA
B C
ABCABC
![Page 6: L A C H B 1 2 Problem. Given two points A, B on the same side of line Find the point C on L such that and make congruent angles with L.](https://reader036.fdocuments.net/reader036/viewer/2022082501/5a4d1b717f8b9ab0599b56f0/html5/thumbnails/6.jpg)
Problem. Given a circle K and a point P on K. Find the locus of midpoints M of all chords PA of K through P .
A
K
K
P
K