Constructions — Flashcards

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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…