Equal sums of surfaces
$begingroup$
The inner points $X$ and $Y$ in the convex quadrilateral $ABCD$ are such that $angle ABX=angle CBY$, $angle BCY=angle DCX$, $angle CDY=angle ADX$ and $angle DAY=angle BAX$.
Prove that $$S^{}_{AXB}+S^{}_{CXD}=S^{}_{AYD}+S^{}_{BYC}$$
euclidean-geometry
edited Jan 6 at 13:41
greedoid
41.9k1152105
asked Jan 6 at 13:17
J. HoltanJ. Holtan
62
$endgroup$
add a comment |
$begingroup$
The inner points $X$ and $Y$ in the convex quadrilateral $ABCD$ are such that $angle ABX=angle CBY$, $angle BCY=angle DCX$, $angle CDY=angle ADX$ and $angle DAY=angle BAX$.
Prove that $$S^{}_{AXB}+S^{}_{CXD}=S^{}_{AYD}+S^{}_{BYC}$$
euclidean-geometry
edited Jan 6 at 13:41
greedoid
41.9k1152105
asked Jan 6 at 13:17
J. HoltanJ. Holtan
62
$endgroup$
$begingroup$
What have you tried so far?
$endgroup$
– Larry
Jan 6 at 13:26
add a comment |
$begingroup$
The inner points $X$ and $Y$ in the convex quadrilateral $ABCD$ are such that $angle ABX=angle CBY$, $angle BCY=angle DCX$, $angle CDY=angle ADX$ and $angle DAY=angle BAX$.
Prove that $$S^{}_{AXB}+S^{}_{CXD}=S^{}_{AYD}+S^{}_{BYC}$$
euclidean-geometry
edited Jan 6 at 13:41
greedoid
41.9k1152105
asked Jan 6 at 13:17
J. HoltanJ. Holtan
62
$endgroup$
The inner points $X$ and $Y$ in the convex quadrilateral $ABCD$ are such that $angle ABX=angle CBY$, $angle BCY=angle DCX$, $angle CDY=angle ADX$ and $angle DAY=angle BAX$.
Prove that $$S^{}_{AXB}+S^{}_{CXD}=S^{}_{AYD}+S^{}_{BYC}$$
euclidean-geometry
euclidean-geometry
edited Jan 6 at 13:41
greedoid
41.9k1152105
asked Jan 6 at 13:17
J. HoltanJ. Holtan
62
edited Jan 6 at 13:41
greedoid
41.9k1152105
asked Jan 6 at 13:17
J. HoltanJ. Holtan
62
edited Jan 6 at 13:41
greedoid
41.9k1152105
edited Jan 6 at 13:41
greedoid
41.9k1152105
edited Jan 6 at 13:41
greedoid
41.9k1152105
41.9k1152105
asked Jan 6 at 13:17
J. HoltanJ. Holtan
62
asked Jan 6 at 13:17
J. HoltanJ. Holtan
62
asked Jan 6 at 13:17
J. HoltanJ. Holtan
62
62
$begingroup$
What have you tried so far?
$endgroup$
– Larry
Jan 6 at 13:26
add a comment |
$begingroup$
What have you tried so far?
$endgroup$
– Larry
Jan 6 at 13:26
$begingroup$
What have you tried so far?
$endgroup$
– Larry
Jan 6 at 13:26
$begingroup$
What have you tried so far?
$endgroup$
– Larry
Jan 6 at 13:26
add a comment |
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$begingroup$
What have you tried so far?
$endgroup$
– Larry
Jan 6 at 13:26