# Math

The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X:

The figure shows a circle with points A and B on it and point C outside it. Side BC of triangle ABC intersects the circle at point X. A tangent to the circle at point A is drawn from point C. Arc AB measures 176 degrees and angle CBA measures 56 degrees.

What is the measure of angle ACB?

32°****
60°
28°
16°

The figure below shows the ideal pattern of movement of a herd of cattle, with the arrows showing the movement of the handler as he moves the herd. The arc the handler makes from the starting point to the return point should be a quarter of a circle:

A sector showing a quarter of a circle is drawn. The radius is marked as 70 feet. The endpoints of the arc of the sector are marked as Starting Point and Return Point. The sector is filled with cattle.

Based on this theory, what distance will the handler move from the starting point to the return point if he creates an arc of a circle of radius 70 feet?

439.6 feet****
3846.5 feet
109.9 feet
1758.4 feet

Circle A has center of (2, 3), and a radius of 5 and circle B has a center of (1, 4), and a radius of 10. What steps will help show that circle A is similar to circle B?

Dilate circle A by a scale factor of 2.*****
Translate circle A using the rule (x + 1, y − 1).
Rotate circle A 180° about the center.
Reflect circle A over the y-axis.

Look at the figure below:

A circle is shown with the center O. OR is a segment joining center O to a point R on the circle. PQ is a line touching the circle in Point R. Line MN is shown intersecting the circle in points S and T.

Which is the tangent to the circle?

Segment RO
Line MN
Line PQ*****
Segment ST

Circle A is shown with a central angle marked 30 degrees and the radius marked 5 inches.

Which of the following could be used to calculate the area of the sector in the circle shown above?

π(5in)30 over 360
π(5in)230 over 360****
π(30in)25 over 360
π(30in)5 over 360

A circle is centered at (−3, 2) and has a radius of 2. Which of the following is the equation for this circle?

(x + 3)2 + (y − 2)2 = 2
(x − 3)2 + (y + 2)2 = 4
(x + 3)2 + (y − 2)2 = 4*****
(x − 3)2 + (y + 2)2 = 2

Tiara buys the pizza shown below:

A circular pizza is shown. The edge of one slice is marked AB.

What does the curve AB represent?

Chord
Arc****
Circumference
Tangent

Which of the following is a step in constructing a circle inscribed in a triangle?

Use a compass to locate the intersection of the midpoint of each side.
Use the perpendicular bisectors to find the center of the circle.****
Use a compass to locate the intersection of the altitude of each side.
Use the angle bisectors to find the center of the circle.

Quadrilateral OPQR is inscribed in circle N, as shown below. Which of the following could be used to calculate the measure of ∠OPQ?

Circle N is shown with a quadrilateral OPQR inscribed inside it. Angle O is labeled x plus 16. Angle P is not labeled. Angle Q is labeled 6x minus 4. Angle R is labeled 2x plus 16.

m∠OPQ + (2x + 16)° = 180°
m∠OPQ = (6x − 4)° + (2x + 16)°
m∠OPQ + (x + 16)° + (6x − 4)°= 360°
m∠OPQ = (x + 16)° + (6x − 4)°****

Alex drew a circle with right triangle PRQ inscribed in it, as shown below:

The figure shows a circle with points P, Q, and R on it forming an inscribed triangle. Side PQ is a chord through the center and angle R is a right angle. Arc QR measures 80 degrees.

If the measure of arc QR is 80°, what is the measure of angle PQR?

50°****
40°
80°
70°

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