Tangents — Flashcards
Kerala Board · Class 10 · Mathematics
20 flashcards for Tangents (Kerala Board Class 10 Mathematics) to test yourself on key terms and facts. Sample: "What is a tangent to a circle? How is it"
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What is a tangent to a circle? How is it formed when a chord approaches a point?
Answer
A tangent to a circle is a line that touches the circle at exactly one point. When we have a chord through points A and X on a circle, and we move point X closer and closer to point A along the circle…
State and prove the fundamental property relating a tangent and radius at the point of contact.
Answer
Property: The tangent at a point to a circle is perpendicular to the radius through that point. Proof: Consider chord AX where X moves closer to A. In triangle OAX (O is center), OA = OX (radii), so …
How do you construct a tangent at a given point on a circle?
Answer
Step 1: Mark the given point on the circle Step 2: Draw the radius from the center to this point Step 3: At the given point, construct a perpendicular to this radius Step 4: This perpendicular line is…
If tangents are drawn at the ends of a diameter of a circle, what can you say about their relationship?
Answer
The tangents drawn at the ends of a diameter are parallel to each other. Proof: Let AB be a diameter. At A, tangent is perpendicular to radius OA. At B, tangent is perpendicular to radius OB. Since O…
What is the relationship between the angle at the center and the angle between tangents at the ends of two radii?
Answer
The angle at the center between two radii and the angle between the tangents at the ends of these radii are supplementary (add up to 180°). In quadrilateral OACB where tangents meet at C: - Angles at…
How many tangents can be drawn from an external point to a circle? Describe the construction method.
Answer
Exactly two tangents can be drawn from an external point to a circle. Construction Method: Step 1: Join the external point P to the center O Step 2: Draw a circle with PO as diameter Step 3: This cir…
Prove that the two tangents drawn from an external point to a circle have equal lengths.
Answer
Given: PA and PB are tangents from external point P to circle with center O. To prove: PA = PB Proof: In triangles OAP and OBP: - OA = OB (radii) - OP = OP (common side) - ∠OAP = ∠OBP = 90° (tangent …
Find the length of tangent from point P to a circle with center O and radius 4 cm, if OP = 5 cm.
Answer
Given: Radius = 4 cm, OP = 5 cm To find: Length of tangent PT Step 1: Draw a diagram showing the right triangle OTP Step 2: Apply Pythagoras theorem in right triangle OTP: OP² = OT² + PT² Step 3: Su…
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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