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Potpourri
Tangent/Chord Properties
Area/Arc Length
Angle Properties
Coord geometry
100
A tool used for measuring the angle of a circle.
What is a Protractor?
100
The radius does this to a chord when they are perpendicular.
Bisects it.
100
A semi-circle has a diameter of 28 inches. What is the area of of the semi-circle?
Area = 98 times Pi square cm (about 307.9 sq cm)
100
This angle is twice the inscribed angle when it intercepts the same arc.
What is a central angle?
100
The equation of a circle is (x-3)2 + (y-7)2 = 36. What are the center and radius of this circle?
Center = (3, 7), radius = 6
200

The longest chord in a circle is called this.

What is a Diameter?

200

In a triangle, the line that connects the tangent and the radius of a circle.

What is the hypotenuse?

200

An annulus has an inner radius of 4 cm and and an outer radius of 10 cm. Find the area of the annulus.

Area = 84 * Pi cm2 (or about 263.9 cm2)

200

All inscribed angles that intercept a semicircle are this.

What are right angles?

200
A circle has a center at the point O(1, -6) and the longest chord in the circle measures 18 inches. Write an equation for the circle.
(x - 1)2 + (y + 6)2 = 81
300

What do we call 2 coplanar circles that share a common center.

They are concentric.

300

If you were to draw two different chords and bisect them, the two bisectors would intersect at this point.

What is the Center of the circle?

300

A circle has a radius of 12ft. A and C are points on the circle and the arc measure of (AC) is 50 degrees. What is the arc length of (AC)?

Arc length = (10/3) * Pi ft or about 10.47 ft.

300

An inscribed angle measures (4x - 15) degrees and a central angle measures (3x + 4) degrees. The two angles intercept the same arc. What is x?

x = 6.8?

300

The equation of a circle is (x - 2)2 + (y - 4)2 = 25. Is the point P(6, 7) on this circle?

Yes it is.

400

A hemispherical fish bowl has radius of 20 cm. The surface of the water in the bowl is a circle with radius of 16 cm. The maximum depth of the water is this.

The maximum depth is 8 cm.

400

Four tangent lines to a circle make this figure when consecutive pairs meet at 90 degree angles.

What is a Square?

400

The length of minor arc AB intercepted by central angle AOB is 20 * Pi inches. The radius of the circle is 25 cm. What is the measure of angle AOB.

arc measure of AOB = 144 degrees.

400

A circle has center at point O. The measure of central angle AOB is 72 degrees. What is the measure of angle ABO?

arc measure of ABO = 54 degrees.

400

Write the equation of a circle with center at the origin and passes through the point P(-6, 5)

x2 + y2 = 61

500

Water is flowing through a pipe with radius 13 cm. The maximum depth of the water is 8 cm. What is the width of the surface of the water. (Hint - this is a chord)

What is 24 cm.?

500

A chord intercepts an arc of 90 degrees. If the radius of the circle is 10 cm then what is the length of the chord?

10 times Sqrt(2) cm or about 14.142 cm.

500

An arc of a circle has a measure of 120 degrees and an arc length of 55 * Pi cm. What is the diameter of the circle?

Diameter = 165 cm.

500

Quadrilateral ABCD lies on a circle O of radius 10 cm. If Angle A measures 100 degrees then what is the arc measure of arc DAB?

arc measure of DAB = 160 degrees.

500

The equation of a circle is (x - 1)2 + (y - 10)2 = 9. Point A is at (1, 13) and point B is at (4, 10). What is the area of the sector swept out between points A and B.

Area = (9/4) * Pi sq units (or about 7.07 sq units)