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In triangle ABC, point X is on side BC such that AX=13,BX=10,CX=10, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

 Jun 7, 2023
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Find the area of triangle ABC.

 

Hello Guest!

 

\(\overline{AC}=\overline{AB}\)

\(\Delta\ ACX\ \equiv \Delta\ ABX\)

\(A_{ABC}=\frac{(\overline{AX}+\overline{CX})\cdot \overline{AX}}{2}=\frac{(10+10)\cdot 13}{2}\\ \color{blue}A_{ABC}=130\)

laugh  !

 Jun 7, 2023

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