Secants, Tangents And Their Properties
NIOS · Class 10 · Maths
Flashcards for Secants, Tangents And Their Properties — NIOS Class 10 Maths. Quick Q&A cards covering key concepts, definitions, and formulas.
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Explore the full setA line touches a circle at exactly one point P. What is it called, and what is P called?
Answer
Step 1: A line touching a circle at exactly one point is a tangent. Step 2: The touching point is the point of contact. Answer: The line is a tangent, and P is the point of contact.
A line cuts a circle at two distinct points A and B. What is it called?
Answer
Step 1: A line intersecting a circle in two distinct points is a secant. Step 2: Since it meets the circle at A and B, it is not a tangent. Answer: The line is a secant.
A point P lies outside a circle. How many tangents can be drawn from P to the circle?
Answer
Step 1: A point outside the circle allows two tangents. Step 2: These two tangents are equal in length. Answer: Two tangents can be drawn from an external point.
A point P lies on a circle. How many tangents can be drawn from P?
Answer
Step 1: A point on the circle gives only one tangent. Step 2: Any other line through P cuts the circle again. Answer: Only one tangent can be drawn.
A point P lies inside a circle. How many tangents can be drawn from P?
Answer
Step 1: A point inside the circle does not allow a tangent. Step 2: Any line through P meets the circle at two points. Answer: No tangent can be drawn.
Why is the radius through the point of contact perpendicular to the tangent?
Answer
Step 1: From the centre O to the tangent line, the shortest distance is the perpendicular. Step 2: The radius through the point of contact gives that shortest distance. Step 3: Therefore the radius is…
Find the length of tangent PT if OP = 5 cm and radius OT = 3 cm.
Answer
Step 1: Use OP^2 = OT^2 + PT^2. Step 2: Substitute values: 5^2 = 3^2 + PT^2. Step 3: 25 = 9 + PT^2. Step 4: PT^2 = 16. Step 5: PT = 4 cm. Answer: PT = 4 cm.
Find the length of each tangent from P if OP = 25 cm and radius = 7 cm.
Answer
Step 1: Use OP^2 = OT^2 + PT^2. Step 2: Substitute values: 25^2 = 7^2 + PT^2. Step 3: 625 = 49 + PT^2. Step 4: PT^2 = 576. Step 5: PT = 24 cm. Step 6: The two tangents from an external point are equal…
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