Online Test — Circles
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
A straight line that intersects a given circle at exactly two separate points is called a...
Tangent
Secant
Radius
Normal
Explanation: By definition, a secant line penetrates a circle at two distinct boundary points.
Question 2 of 10
medium
What is the maximum number of tangent lines that can be drawn from a point located deep inside a circle?
Zero
One
Two
Infinite
Explanation: Any line passing through an interior point will cross the boundary twice, making it a secant.
Question 3 of 10
medium
The angle formed between a tangent line and the radius drawn through its point of contact is always...
45 degrees
60 degrees
90 degrees
180 degrees
Explanation: The radius is strictly perpendicular to the tangent line at its point of contact.
Question 4 of 10
medium
If the distance of an external point P from the center of a circle is 13 cm and the radius is 5 cm, what is the length of the tangent?
8 cm
12 cm
14 cm
18 cm
Explanation: Using Pythagoras: Tangent = sqrt(13 squared - 5 squared) = sqrt(169 - 25) = 12 cm.
Question 5 of 10
medium
Two tangents PA and PB are drawn from point P. If angle APB is 80 degrees, find the central angle AOB.
80 degrees
90 degrees
100 degrees
120 degrees
Explanation: Opposite angles in the tangent quadrilateral are supplementary: 180 - 80 = 100 degrees.
Question 6 of 10
medium
A circle has a radius of 6 cm. An external point is located 10 cm away from the center. What is the length of one tangent segment?
4 cm
8 cm
sqrt(136) cm
16 cm
Explanation: Using Pythagoras: sqrt(10 squared - 6 squared) = sqrt(100 - 36) = sqrt(64) = 8 cm.
Question 7 of 10
medium
If two tangents drawn from external point P to a circle with center O are inclined to each other at 60 degrees, find angle POA.
30 degrees
50 degrees
60 degrees
90 degrees
Explanation: Total angle APB = 60, so half angle APO = 30. In right triangle OAP, angle POA = 90 - 30 = 60 degrees.
Question 8 of 10
medium
Quadrilateral ABCD circumscribes a circle. If AB = 6 cm, BC = 7 cm, and CD = 4 cm, find the length of side AD.
3 cm
4 cm
5 cm
6 cm
Explanation: For a circumscribed quadrilateral, AB + CD = BC + DA. Thus 6 + 4 = 7 + DA, giving DA = 3 cm.
Question 9 of 10
medium
How many parallel tangents can a single circle have at maximum along any chosen directional axis?
One
Two
Three
Four
Explanation: Parallel tangents can only exist at the opposite ends of a single continuous diameter line.
Question 10 of 10
medium
A tangent line segment PQ is 24 cm long. If the radius of the circle is 7 cm, find the distance from center O to point Q.
25 cm
31 cm
23 cm
17 cm
Explanation: Using Pythagoras: Distance = sqrt(24 squared + 7 squared) = sqrt(576 + 49) = 25 cm.