נתון ( ∙ {\displaystyle \bullet } ): A B = A C = X B C = y 7 ∗ P △ A B C = B C {\displaystyle {\begin{aligned}&AB=AC=X\\&BC=y\\&7*P_{\triangle ABC}=BC\\\end{aligned}}}
צ"ל : יחס בין שוקי הבסיס ∠ A B C = ∠ A C B {\displaystyle \angle ABC=\angle ACB}
הוכחה : P △ A B C = 2 x + y P △ A B C = b c 7 ∙ B C = 2 x + y 7 B C = y ∙ y = 2 x + y 7 7 y = 2 x + y 2 x = 6 y x = 3 y △ A E C cos ∠ A C E = A C C E cos ∠ A C E = x 2 3 x = 1 6 ∠ A C E = 80.405 ∘ {\displaystyle {\begin{aligned}&P_{\triangle ABC}=2x+y\\&P_{\triangle ABC}={\frac {bc}{7}}\bullet \\&BC={\frac {2x+y}{7}}\\&BC=y\bullet \\&y={\frac {2x+y}{7}}\\&7y=2x+y\\&2x=6y\\&x=3y\\&\triangle AEC\\&\cos \angle ACE={\frac {AC}{CE}}\\&\cos \angle ACE={\frac {\frac {x}{2}}{3x}}={\frac {1}{6}}\\&\angle ACE=80.405^{\circ }\\\end{aligned}}}
