GEOMETRY

[SANZEED]

SECONDARY GEOMETRY (OWN)
Let a circle $[_{1}$ be drawn through the vertices $A,B$ of $triangle_ ABC$ touching $BC$ at $B$. Similarly drtaw the circle $[_{2}$ passing through $A,C$ touching $BC$ at $C$.Cord $AB$ produces an angle of $45^0$ at the center of $[_{1}$. Cord $AC$ produces an angle of $60^0$ at the center of $[_{2}$.If the radii of $[_{1}$ and $[_{2}$ are 5 & 7 respectively, then find the area of $triangle_ABC$.

[Phlembac Adib Hasan]

$AB=\sqrt{2.5^2\frac {\sqrt {2}-1} {\sqrt {2} } },AC=\sqrt {2.7^2 \frac {1} {2} }$ [cosine rule]

$ \angle ABC=22.5^0, \angle ACB=30^0 $

So $\angle BAC=127.5^0 $

So $ (\triangle ABC)=\frac {1} {2} \sqrt{2.5^2\frac {\sqrt {2}-1} {\sqrt {2} } } \sqrt {2.7^2 \frac {1} {2} }\; sin\; 127.5^0 $.

[nafistiham]

SECONDARY GEOMETRY (OWN)
Let a circle $[_{1}$ be drawn through the vertices $A,B$ of $triangle_ ABC$ touching $BC$ at $B$. Similarly drtaw the circle $[_{2}$ passing through $A,C$ touching $BC$ at $C$.Cord $AB$ produces an angle of $45^0$ at the center of $[_{1}$. Cord $AC$ produces an angle of $60^0$ at the center of $[_{2}$.If the radii of $[_{1}$ and $[_{2}$ are 5 & 7 respectively, then find the area of $triangle_ABC$.

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