In `triangle ABC`,if `AB=sqrt(2),AC=sqrt(20)`,B=(3,2,0),C=(0,1,4) and D is the midpoint of BC then AD=

In /_\ABC ,if AB=sqrt(2),AC=sqrt(20),B=(3,2,0),C=(0,1,4) and D is the midpoint of BC then AD=

In any triangle ABC,prove that AB^(2)+AC^(2)=2(AD^(2)+BD^(2)), where D is the midpoint of BC .

The vertices of a triangle ABC are A (2,3,1) , B(-2, 2,0), and C(0,1,-1). What is the magnitude of the line joining mid points of the sides AC and BC ?

In a triangle ABC,B=90^(@) and D is the mid-oint of BC then prove that AC^(2)=AD^(2)+3CD^(2)

Let area of a triangle ABC is (sqrt(3)-1)/(2) where AC=2,AB=(sqrt(3)-1) and /_A is acute.Find the value of (BC)^(2)

In right-angled triangle ABC in which /_C=90^(@), if D is the mid-point of BC, prove that AB^(2)=4AD^(2)-3AC^(2)

Consider triangle AOB in the x-y plane, where A-=(1,0,0),B-=(0,2,0) and O-=(0,0,0) The new position of O, when triangle is rotated about side AB by 90^(0) can be a.((4)/(5),(3)/(5),(2)/(sqrt(5))) b.((-3)/(5),(sqrt(2))/(5),(2)/(sqrt(5))) c.((4)/(5),(2)/(5),(2)/(sqrt(5))) d.((4)/(5),(2)/(5),(1)/(sqrt(5)))

In ABC, the coordinates of B are (0,0),AB=2,/_ABC=(pi)/(3), and the middle point of BC has coordinates (2,0) .The centroid o the triangle is ((1)/(2),(sqrt(3))/(2))(b)((5)/(3),(1)/(sqrt(3)))(4+(sqrt(3))/(3),(1)/(3))( d) none of these

In a triangle ABC, angleB=90^(@), D is the midpoint of AC, BD=sqrt117 . Sum of sides of AB & BC is 30 cm. Find the area of triangle ABC.