Question

Geometry help please. So I understand that the sum of AB • AP should equal CD • CP but how would I go about finding the value of X? I could put random numbers in the equation until the sums were equal but I figure there's a simpler way of doing this.

Answer 1

CP * DP = AP * BP 

(8 + x + 2)(x + 2) = (5 + x + 3)(x + 3) 
(x + 10)(x + 2) = (x + 8)(x + 3) 
x² + 2x + 10x + 20 = x² + 3x + 8x + 24 
x² + 12x + 20 = x² + 11x + 24 
12x - 11x = 24 - 20
x = 4