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?
A0
B1
C2
DInfinitely many
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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?
A1
B2
C3
D4
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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:
AChord of contact
BAxis of symmetry of the two tangents
CTangent line
DDiameter
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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?
A2
B-1
C0
D1
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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?
A1
B2
C-1
D0
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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.