Main street and washington avenue meet at a right angle. a large park begins at this corner. joe's school lies at the opposite corner of the park. usually joe walks 1.6 miles along main street and then 1.2 miles up washington avenue to get to school. today he walked in a straight path across the park and returned home along the same path. what is the difference in distance between the two round trips?

complete the explanation and enter your answers rounded to the nearest tenth of a mile.

today joe walked 1.62 + 1.22 =
mi each way. he usually walks 1.6 + 1.2 =
mi each way. so the difference is
mi each way.

the difference in distance between the two round trips is
mi.

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