Jenna is planting four circular gardens. She is planting one garden each for tomatoes, carrots, cabbage, and strawberries. Each garden will have a fence around it to keep rabbits out. The tomato, carrot, and cabbage gardens will all be the same size. Since Jenna loves strawberries, the strawberry garden will be larger. It will use the same amount of fencing as the other three gardens combined. She used a total of about 113.04 feet of fencing material. The area of each smaller garden is about ___
square feet.

The area of the larger garden is about
square feet.

The area of the larger garden is ___
times larger than the area of the smaller garden.

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