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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.

Jan 25, 2019
edited by yasbib555  Jan 25, 2019

#1
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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   Jan 25, 2019
#2
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ahhh that makes sense thank you!!

yasbib555  Jan 26, 2019