Online Test — Circles
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
What is the geometric term for a chord that passes directly through the center of a circle?
Radius
Secant
Diameter
Segment
Explanation: The diameter is defined as the special chord that passes through the circle's center.
Question 2 of 10
medium
If a circle has a radius of 13 cm, what is the length of the longest possible chord that can fit inside it?
13 cm
26 cm
39 cm
6.5 cm
Explanation: The longest chord is the diameter, which is equal to 2 × radius = 2 × 13 = 26 cm.
Question 3 of 10
medium
A perpendicular line dropped from the center of a circle splits a 12 cm chord into two segments. How long is each segment?
3 cm
4 cm
6 cm
8 cm
Explanation: The perpendicular from the center bisects a chord, splitting it into two equal halves (12/2 = 6).
Question 4 of 10
medium
Two chords, AB and CD, sit at the exact same perpendicular distance of 4 cm from the center. If AB = 10 cm, find CD.
5 cm
10 cm
20 cm
8 cm
Explanation: Chords that are equidistant from the center of a circle are guaranteed to be equal in length.
Question 5 of 10
medium
In a cyclic quadrilateral ABCD, if Angle B measures 110°, what is the measurement of its opposite angle, Angle D?
110°
90°
70°
180°
Explanation: Opposite angles of a cyclic quadrilateral are supplementary: 180° - 110° = 70°.
Question 6 of 10
medium
How many unique circles can be drawn that pass simultaneously through three separate non-collinear points?
Zero
Exactly one
Exactly two
Infinitely many
Explanation: There is one and only one unique circle passing through three non-collinear points.
Question 7 of 10
medium
A region bound by a single straight chord line and a curved boundary arc is called a:
Sector
Segment
Secant
Semicircle
Explanation: A segment is the space enclosed between a chord and its corresponding arc.
Question 8 of 10
medium
If two chords subtend equal angles at the center of a circle, what can we conclude about the chords?
They are perpendicular
One is double the other
They are equal in length
They are parallel
Explanation: If the center angles are equal, the chords must be equal in length.
Question 9 of 10
medium
A perpendicular line from the center hits a chord at a distance of 3 cm. If the radius is 5 cm, find the total chord length.
4 cm
8 cm
6 cm
10 cm
Explanation: Half-chord = square root of ($5^2 - 3^2$) = 4. Total chord length = 2 × 4 = 8 cm.
Question 10 of 10
medium
If three points A, B, and C lie on a perfectly straight line, how many circles can pass through all three?
1
3
0
Infinite
Explanation: No circle can pass through three collinear points since a circle cannot be a straight line.