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Class 10 Number of Tangents from a Point — practice questions with answers

Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. How many tangents can be drawn to a circle from a point lying OUTSIDE the circle?
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Answer: C) 2
From an external point exactly two tangents can be drawn to a circle.
2. How many common tangents can be drawn to two circles that touch each other EXTERNALLY?
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Answer: C) 3
Two externally touching circles have 3 common tangents: 2 direct and 1 at the point of contact.
3. The two tangents from an external point P to a circle make equal angles with the line joining P to the centre. This line PO is called the:
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Answer: B) Axis of symmetry of the two tangents
PO bisects the angle between the two tangents and is the axis of symmetry of the figure.
4. A circular tabletop of radius 7 cm is being studied by Kabir. He picks a point exactly at the centre of the table.
He asks how many tangents to the circular edge pass through this central point.
What is the answer?
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Answer: C) 0
The centre is inside the circle (distance 0 < radius), so no tangent can pass through it.
5. Two coins of radii 3 cm and 1 cm are placed so that the smaller coin lies entirely inside the larger one, with their centres 1 cm apart (so they do NOT touch and one is fully inside the other).
How many common tangents can be drawn to the two coins?
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Answer: D) 0
Distance between centres (1) < difference of radii (3-1=2), so the smaller circle lies fully inside the larger without touching, giving 0 common tangents.
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