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Another two parallels
jayme   0
14 minutes ago
Dear Mathlinkers,

1. ABCD a square
2. (A) the circle with center at A passing through B
3. P the points of intersection of the segment AC and (A)
4. I the midpoint of AB
5. Q the point of intersection of the segment IC and (A)
6. M the foot of the perpendicular to (AB) through Q.
7. Y the point of intersection of the segment MC and (A)
8. X the point of intersection de (AY) et (BC).

Prove : QX is parallel to AB.

Jean-Louis
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jayme
14 minutes ago
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Ratio of lengths
Sadigly   0
Apr 13, 2025
In a triangle $ABC$, $I$ is the incenter. Line $CI$ intersects circumcircle of $ABC$ at $L$, and it is given that $CI=2IL$. $M;N$ are points chosen on $AB$ such that $\angle AIM=\angle BIN=90$. Prove that $AB=2MN$
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Sadigly
Apr 13, 2025
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Ratio of lengths
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Sadigly
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Sadigly
#1 h  Apr 13, 2025, 7:11 PM
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In a triangle $ABC$, $I$ is the incenter. Line $CI$ intersects circumcircle of $ABC$ at $L$, and it is given that $CI=2IL$. $M;N$ are points chosen on $AB$ such that $\angle AIM=\angle BIN=90$. Prove that $AB=2MN$
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