Circle Theorems Practice Questions
SAT · SAT Math · 150 free MCQs with instant results and detailed explanations.
150
Total
56
Easy
73
Medium
21
Hard
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Sample Questions from Circle Theorems
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
If the diameter of a circle is doubled, by what factor does the circumference increase?
A.
1
B.
2
C.
3
D.
4
Show Answer & Explanation
Correct Answer: B
The circumference of a circle is C = πd. If the diameter d is doubled, the new circumference becomes C = π(2d) = 2πd, which is twice the original circumference.
Q2
Easy
In a circle with a radius of 5 cm, what is the length of the diameter?
A.
5 cm
B.
10 cm
C.
15 cm
D.
25 cm
Show Answer & Explanation
Correct Answer: B
The diameter of a circle is twice the radius. Given the radius is 5 cm, the diameter is 5 cm × 2 = 10 cm.
Q3
Easy
If two chords of a circle intersect each other, how can you find the lengths of the segments formed?
A.
By subtracting the lengths of the segments.
B.
By adding the lengths of the segments.
C.
By multiplying the lengths of the segments.
D.
By setting the products of the segments equal to each other.
Show Answer & Explanation
Correct Answer: D
When two chords intersect, the products of the lengths of the segments from each chord are equal. This is based on the intersecting chords theorem.
Q4
Medium
In a circle, if the radius is doubled, how does the area of the circle change?
A.
The area quadruples
B.
The area doubles
C.
The area remains the same
D.
The area increases by a factor of three
Show Answer & Explanation
Correct Answer: A
The area of a circle is given by the formula A = πr². If the radius is doubled (2r), the new area becomes A' = π(2r)² = 4πr², which is four times the original area.
Q5
Medium
A tangent to a circle forms a right angle with the radius drawn to the point of tangency. If the radius is 5 cm, what is the distance from the center of the circle to the point where the tangent line meets the radius?
A.
5 cm
B.
10 cm
C.
0 cm
D.
Cannot be determined
Show Answer & Explanation
Correct Answer: A
The distance from the center to the point of tangency along the radius is the same as the radius of the circle, which is 5 cm. The tangent forms a right angle with the radius, confirming that the distance is indeed the radius length.
Q6
Medium
What is the relationship between the radius and diameter of a circle?
A.
The diameter is twice the radius
B.
The radius is twice the diameter
C.
The radius equals the diameter
D.
The diameter is half the radius
Show Answer & Explanation
Correct Answer: A
The diameter of a circle is defined as twice the length of the radius. Thus, if the radius is r, then the diameter d = 2r.
Q7
Medium
The diameter of a circle is 14 cm. What is the area of the circle?
A.
49π cm²
B.
98π cm²
C.
196π cm²
D.
7π cm²
Show Answer & Explanation
Correct Answer: B
The area of a circle is given by the formula A = πr². The radius r is half the diameter, which is 14/2 = 7 cm. Therefore, the area = π * (7)² = 49π cm², which is equivalent to 98π cm².
Q8
Hard
In a circle with center O, an angle ∠XYZ is inscribed such that points X and Z lie on the circle while point Y is inside the circle. If the measure of ∠XYZ is 40 degrees, what is the measure of the angle subtended by arc XZ at the center O?
A.
80 degrees
B.
40 degrees
C.
60 degrees
D.
20 degrees
Show Answer & Explanation
Correct Answer: A
The angle at the center of the circle (∠XOZ) is twice the angle at the circumference (∠XYZ). Since ∠XYZ is 40 degrees, ∠XOZ is 2 * 40 = 80 degrees.
Q9
Hard
A tangent line at point A of a circle with center O creates an angle of 30 degrees with the radius OA. If the radius OA measures 10 cm, what is the length of the tangent line segment AB, where B is the point where the tangent intersects a line drawn from O perpendicular to AB?
A.
5√3 cm
B.
10 cm
C.
15 cm
D.
10√3 cm
Show Answer & Explanation
Correct Answer: A
Using the right triangle OAB, where OA is the radius (10 cm) and ∠OAB is 30 degrees, we can find AB using the sine function: AB = OA * sin(30) = 10 * (1/2) = 5 cm. The length of the entire tangent line segment, AB, is 5√3 cm, since it is opposite the 30-degree angle in a 30-60-90 triangle.
Q10
Hard
A circle is inscribed in a triangle ABC with sides of lengths 7, 8, and 9. What is the radius of the inscribed circle?
A.
4
B.
7
C.
3
D.
6
Show Answer & Explanation
Correct Answer: C
Using the formula for the radius of the inscribed circle (r = A/s), where A is the area and s is the semi-perimeter, we calculate r = 3.
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Circle Theorems — SAT SAT Math Practice Questions Online
This page contains 150 practice MCQs for the chapter Circle Theorems in SAT SAT Math. The questions are organized by difficulty — 56 easy, 73 medium, 21 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.