The parallel line of the AC line intersects the sides AB and BC of the triangle ABC, respectively, at the points M and N, AM: MB = 2: 3. The area of the triangle ABC is 125 cm square. Find the area of the AMNC trapezoid.15 POINTS

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

It would have infinite solutions.

To find the x-intercept, make  y  equal to zero, and solve for  x. to find the y-intercept, make  x  equal to zero, and solve for  y.explanation: y=4x−2x-intercept0=4x−2add  2  to both sides of the equation.2=4xdivide both sides by  4.24=xsimplify.12=xswitch sides.x=12y-intercepty=4(0)−2y=−2