Prove that the lengths of the perpendiculars from any point on the bisector of an angle to the sides are equal.

Consider a line with equation x - sqrt 3 y + 4 =0 Reduce the given equation into normal form and find the length of the perpendicular from the origin on the line and the angle made by this perpendicular with the x- axis.

Draw a right triangle and the perpendicular from the midpoint of the of the hypotenuse to the base Prove that in the large triangle the distances from the midpoint of the hypotenuse to all thevertices are equal. .

The perpendicular from the square comers of a right triangle cuts the opposite side into two parts of 2 and 3 cm length. Prove that if the perpendicular from the square corner of the right triangle divides the opposite sides into partsof length a and b and if the length of the perpendicular is h, then h^2= ab .

In the picture, the perpendicular is drawn from the midpoint of the hypotenuse of a right triangle. to the base. Calculate the length of the third side of the large right triangle and the lengths of all three sides of the small right triangle.

Draw a right triangle and the perpendicular from the midpoint of the of the hypotenuse to the base Prove that this perpendicular is half the perpendicular side of the large triangle. .

Draw a right triangle and the perpendicular from the midpoint of the of the hypotenuse to the base Prove that perpendicular bisects the bottom side of the larger triangle. .

Find the length and foot of the perpendicular from the point (7,14,5) to the plane 2x+4 y-z=2 .

The length of the perpendicular drawn from a vertex to opposite side of an equilateral triangle is '12 cm'. Calculate its perimeter and area.