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Geometry Quiz: How well do you know geometry?

Below you will find 5 geometry questions that will test how well you know the subject.  Enjoy yourself as you take on the challenge.

Geometry Quiz

1.Using the figure below, find lengths \(BC\) and \(BD\).

righttria

2. For the following figure, find angles \(a,b\) and \(c\).

angles.png

3. Find the sums of angles \(\angle A+\angle C \) for the following figure.

cyclicquad

4. For the figure below, find the length \(AF\).

cevas.png

 

5. Suppose that a line segment with left endpoint \(A\) and right endpoint \(B\) has length 6 inches.  Choose a point \(P\) on the line segment \(\overline{AB}\).  You then construct a right triangle so that both legs have length \(AP\) and a square that has side length \(PB\) (see figure below, not to scale).  How far from \(A\) should you place \(P\) in order to minimize the sum of the areas of the triangle and the square?
Untitled

Submission

Submit your answers in the form below to be taken to the solutions page.  Here you can see how well you did!

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