Circle Angles and Arcs Test – Geometry Math (Printable PDF)

Question 1 Central and Inscribed (2 points)

Find m∠ACB.

Question 2 Semicircle with Algebra (2 points)

AB is a diameter of a circle and C is on the circle. ∠A = (2x + 9)° and ∠B = (4x + 3)°. Find x and both angles.

Question 3 Tangent Segment (2 points)

A tangent from P touches a circle with center O at T. The radius is 6 and OP = 14. Find PT as a simplified radical.

Question 4 Inscribed Quadrilateral (3 points)

Quadrilateral ABCD is inscribed in a circle. ∠A = (5x − 8)°, ∠C = (3x + 20)°, ∠B = (4y + 3)° and ∠D = (6y − 3)°. Find all four angles.

Question 5 Arcs and Inscribed Angles (3 points)

1. Find arc DA. (1 point)
2. Find m∠BAD. (1 point)
3. Find m∠ACB. (1 point)

Question 6 Congruent Chords with Algebra (3 points)

Chords AB and CD are congruent chords of the same circle. Arc AB = (6x + 4)° and arc CD = (8x − 22)°. Find x, the measure of arc AB, and an inscribed angle that intercepts arc AB.

Question 7 Chord in a Fountain (3 points)

A circular fountain has a radius of 18 feet. A straight pipe forms a chord 24 feet long. How far is the pipe from the center of the fountain? Give the exact value and a decimal to the nearest tenth.

Question 8 Two Tangents (2 points)

Tangents from P touch a circle with center O at A and B, and m∠P = 44°. Find m∠AOB and the measure of the major arc AB.