Prove that the bisectors of the 4 interior angles of a quadrilateral form a cyclic quadrilateral.
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You don't need a nice diagram, a lousy one will do just as well
Let the angles of the original quadrilateral be $2\alpha,2\beta,2\gamma,2\delta$ so that $$\alpha+\beta+\gamma+\delta=180$$
So according to the diagram, the opposite angles in the small quadrilateral add to $180$
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Airdish
Updated on August 01, 2022Comments
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Airdish over 1 year
I can't seem to draw a good diagram for this question. I tried to draw a quadrilateral and draw the angle bisectors, but they intersected to form a very small quadrilateral. Then I tried to draw a cyclic quadrilateral and extend the sides to form an external quadrilateral, but the diagram turned out shoddy. A diagram and perhaps a starting point hint would be greatly appreciated!
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Wojowu almost 8 yearsHint: Letting the angles of original quadrilateral $\alpha,\beta,\gamma,\delta$, try to calculate the angles of small quadrilateral.
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Airdish almost 8 yearsI know that much, but I need a nice diagram.
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Wojowu almost 8 yearsI'm sorry, but I can't help you with that. Try using some computer tool like GeoGebra if you want precise drawings.
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Airdish almost 8 yearsyeah I just did it with a bad diagram, different one from yours. Thanks for the answer though... :)