Jul 19, 2024 · Pentagon $ (ABCDE)$ is inscribed in a circle of radius $1$. If $\angle DEA=\angle EAB = \angle ABC$ and $m\angle CAD=60^ {\circ}$ and $BC=2AB$. Compute the area of ...

Jun 18, 2020 · E is a point inside square ABCD such that $\angle {ECD} = \angle {EDC} = 15.$ Find $\angle {AEB}.$ I drew a picture for this but I don't know how to continue. Any ...

Apr 10, 2013 · If $A$ and $B$ are $n\\times n$ matrices such that $AB = BA$ (that is, $A$ and $B$ commute), show that $$ e^{A+B}=e^A e^B$$ Note that $A$ and $B$ do NOT have to be ...

Sep 10, 2020 · I had the following problem in my book- $$ abc + bcd + cde + dea + eab \le5 $$ which is to be proved for non - negative real numbers satisfying $a + b + c + d + e = 5$.

Jun 11, 2023 · Prove that triangle $EDC$ is similar to triangle $EAB$, given $CD$ is parallel to $AB$, and specify a reason for similarity. I deduce that triangles $ACE$ and $CDE$ have common height, …

Oct 16, 2020 · Alternatively, there is a pretty easy way: First since $\angle DAF=\angle CDE=\angle EAB$ we know $\angle DAE=\angle FAB$. Second since $A,F,E,B$ are co-cyclic we know $\angle …

Feb 1, 2017 · A pentagon ABCDE contains 5 triangles whose areas are each one. The triangles are ABC, BCD, CDE, DEA, and EAB. Find the area of ABCDE? Is there a theorem for ...

Sep 22, 2020 · So we take the lines from centroids of $\triangle CDE, \triangle DEA, \triangle EAB$ through point $\overline {p}$ and show each of them is perpendicular to the line segment made by …

Apr 5, 2017 · A given convex pentagon $ABCDE$ has the property that the area of each of the five triangles $ABC$, $BCD$, $CDE$, $DEA$, and $EAB$ is unity. calculate the area of the ...

Sep 14, 2015 · $\triangle AEB$ is equilateral, so $|AE|=|AB|=|AD|$. Hence $\triangle DAE$ is isosceles, so $\angle ADE = \angle AED$, and so $\angle ADE = \frac {1} {2} (\pi-\frac {\pi} {6}) = 5\pi/12$. The …