BB_1 is the angle bisector of triangle ABC, and I is its incenter. The perpendicular bisector of segment AC intersects the circumcircle of triangle AIC at D and E. Point F is on the segment B_1C such that AB_1=CF. Prove that the four points B, D, E and F are concyclic.

How is the number of vertices for a prism related to the name of the prism

The length of a rectangle is x times the square root of 100. the width is one-half y more than three-halves x. given that the area of the rectangle is 125 cm2, which equation could represent the rectangle in terms of x and y? a) 5xy − 15x = 125 b) 5xy + 15x = 125 c) 15x2 − 5xy = 125 d) 15x2 + 5xy = 125

Write the point-slope form of the line passing through (2, -12) and parallel to y=3x.