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### Find the segment "DC" in the obtuse triangle below

Let $R$ be the midpoint of $AQ$, so $\lvert AR\rvert = \lvert RQ\rvert = 5$. Since $\triangle ADQ$ is right-angled, then $AQ$ is the diameter of its circumcircle, so $R$ is its center, which means ...
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For simpler algebra, let $$\lvert BA \rvert = \lvert BC \rvert = \lvert CD \rvert = x \;\;\to\;\; \lvert AC \rvert = \sqrt{2}x$$ Next, we just need to use your result of $\measuredangle ADC = 135^{\... • 50.2k 1 vote Accepted ### Find$∡𝐶$in a right triangle$ABC$below Since$\triangle ABC$is right-angled, then the midpoint of$AC$, call it$O$, is the center of the circumscribed circle, with radius$r$, of$\triangle ABC$. Also, let $$\vert CD\rvert = 2x$$ Next, ... • 50.2k 1 vote ### Calculate the angle$x$in the quadrilateral$ABCD$I am trying to give more solutions to the present question. But first of all, there will be some comments, the solutions depend on them. The problem has a setting of the shape "Here is a picture ... • 34.4k 1 vote ### Primal and dual configuration of point-line Given: Point$p = (a, b)$in the primal space corresponds to the line$ p^* = \{ (x, y) \mid y = ax - b \}$in the dual space. Line$\ell = \{ (x, y) \mid y = mx - n \}$in the primal space ... • 468 1 vote Accepted ### Circle geometry - angle at centre theorem Let a circle with center$C$pass through points$P$,$Q$,$R$, and$S$in that sequence, where$PQ$is parallel to$RS$. Let$X$be the intersection of the lines$\overline{PR}$and$\overline{QS}\$. ...
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