Practice solving high school geometry problems involving circles, including arc measures, central and inscribed angles, tangent lines, chord relationships, sector area, and equations of circles.
Read each problem carefully. Show your work in the space provided. Use exact answers in terms of pi when requested, and round only when the problem tells you to.
Angles, arcs, chords, tangents, and circle equations
Geometry - Grade 9-12
- 1
A circle has radius 7 cm. Find its circumference and area. Leave both answers in terms of pi.
- 2
In circle O, central angle AOB measures 128 degrees. What is the measure of minor arc AB?
- 3
An inscribed angle intercepts an arc that measures 86 degrees. Find the measure of the inscribed angle.
- 4
Points A, B, C, and D lie on a circle. If angle ABC measures 52 degrees, what is the measure of arc AC that does not contain point B?
- 5
A tangent line touches a circle at point T. Radius OT is drawn to the point of tangency. If angle OTP is formed by the radius and the tangent line, find its measure.
- 6
From the same external point P, two tangent segments are drawn to a circle. The tangent segments are PA and PB. If PA = 3x + 4 and PB = 5x - 10, find x and the length of each tangent segment.
- 7
A chord is 16 inches long and is 6 inches from the center of a circle. Find the radius of the circle.
- 8
Two chords intersect inside a circle. One chord is split into segments of lengths 4 and 15. The other chord is split into segments of lengths 6 and x. Find x.
- 9
Two secants are drawn from the same external point. The first secant has an external segment of 5 and a whole length of 20. The second secant has an external segment of 8 and a whole length of x. Find x.
- 10
A tangent and a secant are drawn from the same external point. The tangent segment is 12 units long. The secant has an external segment of 8 units and a whole length of x units. Find x.
- 11
Find the length of a 60 degree arc in a circle with radius 9 cm. Leave your answer in terms of pi.
- 12
Find the area of a sector with central angle 120 degrees in a circle with radius 6 meters. Leave your answer in terms of pi.
- 13
Write the equation of a circle with center (3, -2) and radius 5.
- 14
Find the center and radius of the circle given by the equation (x + 4)² + (y - 1)² = 49.
- 15
Complete the square to write x² + y² - 6x + 8y - 11 = 0 in standard form. Then identify the center and radius.