What is the reason for statement 7 in the given proof?

definition of midpoint
definition of slope
parallel lines have equal slopes.
using point-slope formula

I didn't read through the entire proof but it appears the obvious answer by deduction is D: using the point slope formula.

The proof is about finding the slope of AE BF and CD, so midpoints have nothing to do with it.

It's also not the definition of a slope and it also doesn't have to do with parallel lines because it mentions none of it in previous statements.

Thus the answer is using the point-slope formula as the previous statement was entirely dedicated to finding the coordinates for the points. All statement 7 did was to plug those values in to get the slope.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

Wow. that is a really cool question.