On the sides of a triangle ABC, squares ABDE, ACFG, BCJK are constructed externally to it. BF, AJ, CD, AK are joined. If FC, DB are produced to meet AJ, AK in H, I respectively and X, Y are the intersections of BF, CD with AC, AB respectively, show that X, H are equidistant from C and Y, I are also equidistant from B. Prove also that the perpendiculars from A, B, C on GE, DK, FJ respectively intersect in the centroid of the triangle ABC and that GE, DK, FJ are respectively double the medians from A, B, C. E D F R K
On the sides of a triangle ABC, squares ABDE, ACFG, BCJK are constructed externally to it. BF, AJ, CD, AK are joined. If FC, DB are produced to meet AJ, AK in H, I respectively and X, Y are the intersections of BF, CD with AC, AB respectively, show that X, H are equidistant from C and Y, I are also equidistant from B. Prove also that the perpendiculars from A, B, C on GE, DK, FJ respectively intersect in the centroid of the triangle ABC and that GE, DK, FJ are respectively double the medians from A, B, C. E D F R K
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:On the sides of a triangle ABC, squares ABDE, ACFG, BCJK are
constructed externally to it. BF, AJ, CD, AK are joined. If FC, DB are
produced to meet AJ, AK in H, I respectively and X, Y are the intersections
of BF, CD with AC, AB respectively, show that X, H are equidistant from C
and Y, I are also equidistant from B. Prove also that the perpendiculars from
A, B, C on GE, DK, FJ respectively intersect in the centroid of the triangle
ABC and that GE, DK, FJ are respectively double the medians from A, B, C.
G
F
R
M
J
K
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