Geometry — Quiz 5

Questions in this quiz (7)

1. A tangent is drawn to a circle from an external point that is 25 inches from the center of the circle. If the external point is 15 inches from the point of tangency, what is the radius of the circle?

   • $$34\sqrt{5}$$
   • $$25$$
   • $$5\sqrt{34}$$
   • $$20$$

2. A security camera is mounted on the ceiling 6 feet from one wall of a hallway and 8 feet from the adjacent wall. How many feet is the camera from the intersection of the two walls?

   • $$28$$
   • $$2\sqrt{7}$$
   • $$10$$
   • $$36$$

3. In parallelogram ABCD, angle A is 3 times angle B. What is the measure in degrees of angle A?

   • 60
   • 135
   • 120
   • 150

4. Let triangle $$EFG$$ have the following properties:$$\angle EFG = 52^\circ$$, $$\angle EGF = 38^\circ$$, and $$FG = 6.4 \text{ cm}$$Let point $$A$$ be the midpoint of segment $$FG$$. Calculate the distance $$AE$$.

   • 3.2
   • 5
   • 6.4
   • 4.2

5. Triangle $$ABC$$ is a right triangle with the right angle at $$B$$, where: $$AB = 6$$ and $$AC = 10$$. Let $$K$$ be the perpendicular projection of point $$B$$ onto the line segment $$AC$$. Let $$BK = x$$Determine the value of $$x$$.

   • $$\frac{1}{2}$$
   • $$\frac{18}{5}$$
   • $$\frac{36}{5}$$
   • $$\frac{24}{5}$$

6. Let $$ABC$$ be a triangle and $$H$$ the perpendicular projection of point $$A$$ onto the segment $$BC$$, where:AC = 20, AB = 13, BH = 5, H ∈ [BC]Calculate the area of triangle $$ABC$$.

   • 144
   • 192
   • 256
   • 126

7. Given triangle XYZ with each condition below, determine in which cases XYZ is a right triangle.1. The ratio of the three angles is $$2:3:4$$.2. The ratio of the three sides is $$5:12:13$$.3. $$x^2 = y^2 + z^2 - 2yz\cos\theta$$ where $$\theta = 90^\circ$$

   • 1, 2, 3
   • 1, 3
   • 1, 2
   • 2, 3