1. In the trapezoid shown, the ratio of the area of triangle ABC to the area of triangle ADC is 7:3. If AB+CD=210 cm, how long is segment \(\overline{AB}\)?

Diagram: https://latex.artofproblemsolving.com/0/e/3/0e35b9b9988bc071fa41938e3b1a1998b41133db.png

2. Triangle PAB is formed by three tangents to circle O and \(\angle APB = 40^\circ\). Find \(\angle AOB \).

Diagram: https://latex.artofproblemsolving.com/0/a/5/0a51e852055089b5a497559e465f54972f5f5b58.png

3. In the circle with center Q, radii AQ and BQ form a right angle. The two smaller regions are tangent semicircles, as shown. The radius of the circle with center Q is 14 inches. What is the radius of the smaller semicircle? Express your answer as a common fraction.

Diagram: https://latex.artofproblemsolving.com/6/a/6/6a63e76134308c5ec5a40a3adb6b7219a8dd1d93.png

yasbib555 Jan 25, 2019

#1**+1 **

1. In the trapezoid shown, the ratio of the area of triangle ABC to the area of triangle ADC is 7:3. If AB+CD=210 cm, how long is segment AB ?

Triangles ABC and ADC are under the same altitudes....so.....their bases are to each other as their areas...

So.....the base length of ABC is (7/10) of 210 cm = 147 cm = AB

CPhill Jan 25, 2019