Given a non-isosceles triangle with incenter and circumcircle . Denote the midpoints of arcs that does not contain the opposite vertex by respectively. Denote the midpoint of arc containing . Denote the intersection of and as and the intersection of and as . Prove that
Quadrilaterals and are kites.
are collinear and is perpendicular to .
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They are two cyclic kites meaning symmetric pair of angles are right,which directly implies the second property
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Yea even i did it that way ... although in the second part i could first prove the second statement and then the collinearity. This was a nice geometry problem @Alan Yan Can you also post some more geometry problems ?
I m not able to understand the location of point N as intersection of BC and CP makes point C as point N