Constructions
ICSE · Class 10 · Mathematics
Flashcards for Constructions — ICSE Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedA circle has centre O and an external point P. How many tangents can be drawn from P to the circle?
Answer
Step 1: Check the position of point P. Step 2: If the point is outside the circle, two tangents can be drawn. Answer: Two tangents can be drawn from an external point to a circle.
A point lies on the circle. How many tangents can be drawn from that point?
Answer
Step 1: Identify the position of the point. Step 2: A point on the circle has only one tangent. Answer: Only one tangent can be drawn.
A point lies inside the circle. How many tangents can be drawn from that point?
Answer
Step 1: Identify the position of the point. Step 2: A point inside the circle does not allow any tangent. Answer: No tangent can be drawn.
Construct tangents to a circle from an external point P. What is the first construction step?
Answer
Step 1: Join the centre O of the circle to the external point. Step 2: Draw segment OP. Reason: OP is needed to locate the midpoint and build the auxiliary circle later.
Construct tangents to a circle from an external point P. What is the second construction step?
Answer
Step 1: Draw the right bisector of OP. Step 2: Let it intersect OP at M. Reason: M is the midpoint of OP and will be the centre of the auxiliary circle.
Construct tangents to a circle from an external point P. What is the third construction step?
Answer
Step 1: Take M as centre. Step 2: Use radius OM = PM. Step 3: Draw a circle to intersect the given circle at A and B. Answer: The auxiliary circle helps locate points A and B for the tangents.
Construct tangents to a circle from an external point P. What is the final step?
Answer
Step 1: Join PA and PB. Step 2: These lines touch the given circle at A and B. Answer: PA and PB are the required tangents.
Why is M taken as the centre of the auxiliary circle in the tangent construction?
Answer
Step 1: M is the midpoint of OP. Step 2: So OM = PM. Step 3: A circle with centre M and radius OM = PM passes through both O and P. Answer: This makes it possible to find points A and B on the given c…
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