A triangle circled around it

[Rebeka]

rump. 1. PointS. is the center of a circle circumscribed by an acute triangle A B C. Prove that the sum of the angle measuresA B S and A CB is equal 90∘.
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rump. 2. The basisA B isosceles triangle A B C has a length 6and shoulder length 5. Calculate the perimeter of a triangle with an area27which is similar to a triangle A B C.

[radagast]

rump. 1. PointS. is the center of a circle circumscribed by an acute triangle A B C. Prove that the sum of the angle measuresA B S and A CB is equal 90∘.

\(x+2 \gamma +x=\pi \So \gamma +x= \frac{ \pi }{2} \)

[radagast]

rump. 2. The basisA B isosceles triangle A B C has a length 6and shoulder length 5. Calculate the perimeter of a triangle with an area27which is similar to a triangle A B C.

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\(|CH|= \sqrt{25x^2-9x^2}=4x \)
\(27= \frac{6x \cdot 4x}{2} \So x= \frac{3}{2} \)

\(p=2 \cdot 5x+6x=16x=16 \cdot \frac{3}{2} =24\)