Proof 1/r = 1/a +1/b + 1/c Incircle

Let r be the radius of the incircle of triangle ABC, and a, b, c be the radii of the excircles opposite vertices A,B, and C respectively. Write a proof illustrating the fact that 1/r = 1/a +1/b + 1/c. Please do not just direct me to a web page. I would like a detailed breakdown step by step on how this is done. Thanks much!

Centroid of Triangular Region- Balance Point

Using GEOMETRY only, I need to prove that the centroid of a triangular region (assuming uniform density) is the balance point. Trick is that I can't use the "equal areas" argument. I need a step-by-step explanation so I can walk through the process. Please don't send me to a website as I can do that for free. Thanks much!!

Area of a quadrilateral

What is the area of a quadrilateral with sides of length 16, 12, 15, and 25, and a right angle between the sides with lengths 16 and 12?

Pre calc

Need equation for: Ellipse Center at(0,4); focus at(8,4); vertex at (6,7)

pre-calc

Find equation for parabola: focus at (11,7) and vertex at (6,7)

Pre-calc

Find equation for hyperbola with center at (4,9); a=5; c=13; traverse axis parallel to the x axis

Conics

See attachment with questions for 4 equations please

Area of Parallelogram

1. Find the area of parallelogram ABCD, given that AB = BE = ED = 1, and angle ABE = 90 degrees. See attached file for full problem description.

Prove that the centroid is the balance point of a triangle

Need to prove that the centroid is the balance point of a triangle using only GEOMETRY with no vector addition allowed and I can't use the "equal areas" argument as far as the 6 triangles that are made with the medians. Thanks much

Area of quadrilateral

The perimeter of a building is 74'by 59'by 103'by 121'. How can the square footage of the building be calculated?