Circles: Chords, Arcs and Inscribed Angles: Geometry Math Test – PDF Download

Question 1: Similar circles (2 points)

Circle \(P\) has radius 6 and circle \(Q\) has radius 15.

1. A translation followed by a dilation maps \(P\) onto \(Q\). Find the scale factor. (1 point)
2. The circumference of \(P\) is \(12\pi\). Find the circumference of \(Q\). (1 point)

Question 2: Central and inscribed angles (2 points)

In the circle, arc \(AB\) measures \(124^{\circ}\). Point \(O\) is the center and \(C\) is on the circle.

1. Find \(m\angle AOB\). (1 point)
2. Find \(m\angle ACB\). (1 point)

Question 3: Inscribed angle algebra (2 points)

An inscribed angle measures \((5x+2)^{\circ}\) and intercepts an arc that measures \((12x-12)^{\circ}\). Find \(x\) and the measure of the angle.

Question 4: Triangle in a semicircle (2 points)

Segment \(AB\) is a diameter of length 26. Point \(C\) is on the circle with \(AC=10\).

1. Find \(m\angle ACB\). (1 point)
2. Find \(BC\). (1 point)

Question 5: Tangent and radius (3 points)

Segment \(PT\) is tangent to the circle with center \(O\) at \(T\). The radius is 9 and \(OP=15\).

1. Find \(m\angle OTP\). (1 point)
2. Find \(PT\). (1 point)
3. If \(m\angle TOP=53^{\circ}\), find \(m\angle OPT\). (1 point)

Question 6: Tangents from a point (2 points)

Tangent segments \(PA\) and \(PB\) touch a circle at \(A\) and \(B\), and \(m\angle APB=64^{\circ}\).

1. Find the measure of minor arc \(AB\). (1 point)
2. Find the measure of major arc \(AB\). (1 point)

Question 7: Chord and center (2 points)

A chord of length 40 is drawn in a circle with radius 25. Find the distance from the center of the circle to the chord.

Question 8: Inscribed quadrilateral (3 points)

Quadrilateral \(ABCD\) is inscribed in a circle. The angles are \(m\angle A=(3x+15)^{\circ}\), \(m\angle B=(4y+2)^{\circ}\), \(m\angle C=(5x-3)^{\circ}\) and \(m\angle D=(2y+22)^{\circ}\). Find \(x\), \(y\) and the measure of each angle.

Question 9: Skating rink (2 points)

A circular skating rink is 60 feet across. Maya stands at \(A\) and Jamal stands at \(B\), at opposite ends of a diameter. Noah stands at \(N\) on the edge of the rink, 36 feet from Maya.

1. Find the measure of the angle formed by Noah’s lines of sight to Maya and Jamal. (1 point)
2. How far is Noah from Jamal? (1 point)

⬇ Download the Geometry Circles: Chords, Arcs and Inscribed Angles test (PDF, 98 KB)

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