Question

Triunghiul isoscel ABC (AB egal AC) are AB egal 25 cm si BC egal 40 cm.
a)Calculati aria triunghiului ABC.
b)Determinati raza cercului circumscris triunghiului ABC.

Answer 1

ΔABC, AB = AC, AB = 25, BC = 40
Aabc = ?
Rcerc circumscris = R = ?
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Aabc = $\frac{BC*h}{2}$
h = AD, D∈ BC
AD = $\sqrt{ AB^{2} - ( \frac{BC}{2})^2 }$ = $\sqrt{625 - 400} = \sqrt{225}$ = 15
Aabc = $\frac{40 * 15}{2}$ = 300

R = $\frac{AB * AC * BC}{4Aabc} = \frac{25 * 25 * 40}{4 * 300}$ = 20.833