Tetraedru special

[Marius Mainea]

Se da tetraedrul (ABCD) in care \( m(\angle{ABD})=m(\angle{DBC})=30^{\circ} \) , \( AB=BC=2\sqrt{3} \)cm si triunghiul ADC este echilateral cu \( DC=\sqrt{6} \)cm.

a) Demonstrati ca \( (ABD)\perp(BDC) \).

b) In cazul in care \( m(\angle{ADB})<90^{\circ} \) , calculati \( d(B,(ADC)). \)

[Marius Mainea]

a) \( m\angle{D}=45^{\circ} \) ,\( AC\perp BD \) , \( \triangle{ABD}\eq\triangle {CBD} \), etc.

b) Se calculeaza volumul in doua moduri.