pedal circle passes through the anti steiner point?
Given a triangle $triangle ABC$ and $P$ is an arbitrary point. Let $triangle DEF$ be the cevian triangle of $P$ with respect to (wrt) $triangle ABC$ and $triangle XYZ$ be the pedal triangle of $P$ wrt $triangle ABC$. Is it true that the circumcircle of $triangle XYZ$ intersects the circumcirle of $triangle DEF$ at the Poncelet point of $A, B, C, P$ and the Anti Steiner point of $P$ wrt $triangle DEF$? If so, how can we prove it?
geometry euclidean-geometry triangle
asked Oct 12 at 13:54
apple
74515
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Given a triangle $triangle ABC$ and $P$ is an arbitrary point. Let $triangle DEF$ be the cevian triangle of $P$ with respect to (wrt) $triangle ABC$ and $triangle XYZ$ be the pedal triangle of $P$ wrt $triangle ABC$. Is it true that the circumcircle of $triangle XYZ$ intersects the circumcirle of $triangle DEF$ at the Poncelet point of $A, B, C, P$ and the Anti Steiner point of $P$ wrt $triangle DEF$? If so, how can we prove it?
geometry euclidean-geometry triangle
asked Oct 12 at 13:54
apple
74515
add a comment |
Given a triangle $triangle ABC$ and $P$ is an arbitrary point. Let $triangle DEF$ be the cevian triangle of $P$ with respect to (wrt) $triangle ABC$ and $triangle XYZ$ be the pedal triangle of $P$ wrt $triangle ABC$. Is it true that the circumcircle of $triangle XYZ$ intersects the circumcirle of $triangle DEF$ at the Poncelet point of $A, B, C, P$ and the Anti Steiner point of $P$ wrt $triangle DEF$? If so, how can we prove it?
geometry euclidean-geometry triangle
asked Oct 12 at 13:54
apple
74515
Given a triangle $triangle ABC$ and $P$ is an arbitrary point. Let $triangle DEF$ be the cevian triangle of $P$ with respect to (wrt) $triangle ABC$ and $triangle XYZ$ be the pedal triangle of $P$ wrt $triangle ABC$. Is it true that the circumcircle of $triangle XYZ$ intersects the circumcirle of $triangle DEF$ at the Poncelet point of $A, B, C, P$ and the Anti Steiner point of $P$ wrt $triangle DEF$? If so, how can we prove it?
geometry euclidean-geometry triangle
geometry euclidean-geometry triangle
asked Oct 12 at 13:54
apple
74515
asked Oct 12 at 13:54
apple
74515
edited Oct 12 at 14:51
user585792
asked Oct 12 at 13:54
apple
74515
asked Oct 12 at 13:54
apple
74515
asked Oct 12 at 13:54
apple
74515
74515
add a comment |
add a comment |
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