Greg built a plane model. The initial weight of Greg's model was 21.8 pounds. He added a propeller that weighed of the initial weight of the model. Greg estimates that the total
weight of the model with the propeller is about 24 pounds. Is Greg's estimate of the total
weight of the model reasonable?
Greg built another model. The initial weight of this model was 22.7 pounds. He added wings
that weighed of the initial weight of the model. Greg estimates that the total weight of the
model with the wings is about 27 pounds. Is Greg's estimate of the total weight of the model
reasonable?
5

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