![]() We consider the four triangles built with $K$ as one vertex, and with one side of the quadrilateral, then compute their areas. Let now $K\in AC$ be the center of the circle which is tangent to all sides. The area of the quadrilateral is half of the area of the rectangle with sides parallel to the diagonals $AC,BD$, where the sides are passing through $A,B,C,D$, so it is $\frac 12 24\cdot 21=12\cdot 21=252$. So the diagonals of the triangle are $BD=24$, and $AC=AO OC=5 16=21$. The second triangle has the known sides $20$, $12$, so $CO=16$. The perimeter of a polygon is the distance around the outside of the polygon.A polygon is 2-dimensional however, perimeter is 1-dimensional and is measured in linear units.To find the perimeter of a polygon, take the sum of the length of each side.To find the area of a regular polygon, all you have to do is follow this simple formula: area 1. The first triangle has the known sides $13$, $12$, so $AO=5$. Now we consider the triangles $\Delta AOB$ and $\Delta COB$, both with a right angle in $O$. It follows that the given quadrilateral has perpendicular diagonals $AC$, $BD$, they intersect in $O$, the mid point of the segment $BD$. This implies that the side bisector of the given diagonal $BD$ is also the median, and angle bisector in the two triangles. Now we can draw two radii from the center of the circle to points A and B on the edge of the circle. ![]() School Oxford University Course Title MATH Math A Uploaded By WalterWalterWalter. A circumscribed angle is the angle made by two intersecting tangent lines to a circle. ![]() Note that the triangles $\Delta ABD$ and $\Delta CBD$ are isosceles in $A$ and $C$. In the figure abcd is a circumscribed quadrilateral.
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