Constructions
ICSE · Class 10 · Mathematics
Flashcards for Constructions — ICSE Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
What is a tangent to a circle?
Answer
A tangent to a circle is a straight line that touches the circle at exactly one point. This point where the tangent touches the circle is called the point of tangency. The tangent is perpendicular to
How many tangents can be drawn from an external point to a circle?
Answer
Exactly two tangents can be drawn from an external point to a circle. These two tangents are equal in length and make equal angles with the line joining the external point to the center of the circle.
How many tangents can be drawn from a point on the circle?
Answer
Only one tangent can be drawn from a point that lies on the circle. This tangent passes through the point on the circle and is perpendicular to the radius at that point.
How many tangents can be drawn from a point inside the circle?
Answer
No tangent can be drawn from a point that lies inside the circle. This is because any line passing through an interior point will intersect the circle at two points, making it a secant, not a tangent.
What is the first step in constructing tangents from an external point P to a circle with center O?
Answer
The first step is to join the center O of the circle to the external point P. Draw the line segment OP.
After joining OP, what is the second step in tangent construction?
Answer
The second step is to draw the perpendicular bisector of line segment OP. This perpendicular bisector will intersect OP at its midpoint M.
What radius should be used when drawing the circle with center M in tangent construction?
Answer
Use radius OM (or PM, as they are equal since M is the midpoint of OP). Taking M as center and OM as radius, draw a circle that will intersect the given circle at two points.
If the circle with center M intersects the given circle at points A and B, how do you complete the tangent construction?
Answer
Join the external point P to points A and B. The line segments PA and PB are the required tangents to the circle from the external point P.
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Constructions covers several key topics that are frequently asked in ICSE Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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