Kerala SSLC · Mathematics · Class 10
Circles: Important Questions with Answers
These are 10 important multiple-choice questions from the Kerala SSLC Mathematics chapter “Circles” (Kerala SCERT syllabus). Each one shows the correct answer and a short explanation of why it is right. Try answering before you read the answer. ExamSummary has 20 practice questions on this chapter in total.
Q1.How many tangents can be drawn to a circle from a point lying on the circle?
- A)One
- B)Two
- C)Three
- D)Zero
Answer: A) One
A tangent intersects the circle at exactly one point, which is the point of contact. Therefore, there is only one unique tangent possible at any specific point on the circumference.
Q2.What is the angle between the radius of a circle and the tangent at the point of contact?
- A)45°
- B)60°
- C)90°
- D)180°
Answer: C) 90°
According to the fundamental theorem of tangents, the tangent at any point of a circle is perpendicular to the radius through the point of contact. Thus, the angle formed is always 90 degrees.
Q3.Two tangents PA and PB are drawn from an external point P to a circle with center O. If PA = 6 cm, what is the length of PB?
- A)3 cm
- B)6 cm
- C)9 cm
- D)12 cm
Answer: B) 6 cm
The lengths of tangents drawn from an external point to a circle are equal in measure. Therefore, since PA is 6 cm, PB must also be 6 cm.
Q4.What is the maximum number of parallel tangents a circle can have?
- A)One
- B)Two
- C)Four
- D)Infinite
Answer: B) Two
A circle can have exactly two parallel tangents, which touch the circle at the endpoints of the same diameter. Any other orientation would result in intersection or non-contact.
Q5.From a point located inside a circle, how many tangents can be drawn to the circle?
- A)One
- B)Two
- C)None
- D)Infinite
Answer: C) None
By definition, a tangent must touch the circle at exactly one point without entering it. Lines passing through an interior point will intersect the circle at two distinct points, making tangency impossible.
Q6.In the quadrilateral formed by two tangents and their corresponding radii from the center, what is the sum of the measures of opposite angles?
- A)90°
- B)180°
- C)270°
- D)360°
Answer: B) 180°
The two angles where the tangents meet the radii are both 90°. For the quadrilateral to close, the sum of the remaining pair of opposite angles (center and external point) must be 180°.
Q7.If a line touches a circle at exactly one point, the angle between the radius at that point and the line is...
- A)45°
- B)60°
- C)90°
- D)180°
Answer: C) 90°
By the fundamental theorem of tangents, the tangent at any point of a circle is perpendicular to the radius through the point of contact. Therefore, the angle formed is always 90 degrees.
Q8.Two tangents PA and PB are drawn from an external point P to a circle with center O. If ∠AOB = 110°, what is the measure of ∠APB?
- A)60°
- B)70°
- C)80°
- D)90°
Answer: B) 70°
In quadrilateral OAPB, the angles at A and B are 90°. Since the sum of angles in a quadrilateral is 360°, ∠APB = 360° - 90° - 90° - 110° = 70°.
Q9.The length of the tangent drawn from an external point to a circle is always...
- A)Greater than the radius
- B)Less than the radius
- C)Equal to the other tangent from the same point
- D)Equal to the diameter
Answer: C) Equal to the other tangent from the same point
According to the theorem, the lengths of tangents drawn from an external point to a circle are equal in length. This applies regardless of the circle's size.
Q10.How many tangents can be drawn to a circle from a point lying strictly inside the circle?
- A)One
- B)Two
- C)Zero
- D)Infinite
Answer: C) Zero
A tangent intersects the circle at exactly one point. Any line passing through an internal point will intersect the circle at two distinct points, making it a secant, not a tangent.
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