Class 10 • Maths • Chapter 10
CIRCLES
True & False Quiz
Tangent. Radius. Touch.
✓True
✗False
25
Questions
|
Ch.10
Chapter
|
X
Class
Why True & False for CIRCLES?
How this format sharpens your conceptual clarity
🔵 Circle theorems are one of the most proof-heavy sections in Class X — tangent properties appear in almost every Board exam.
✅ T/F tests tangent perpendicularity, equal tangent lengths from external point, and angle in a semicircle.
🎯 The tangent at a point is perpendicular to the RADIUS at that point — not to the chord or diameter.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
A tangent to a circle is a line which touches the circle at exactly one point.
Q 2
Every radius of a circle is a tangent to the circle.
Q 3
A line which cuts a circle at two distinct points is called a secant of the circle.
Q 4
A line which does not intersect a circle at all is called a tangent of the circle.
Q 5
The point where a tangent touches the circle is called the point of contact.
Q 6
The tangent at any point of a circle is perpendicular to the radius drawn to the point of contact.
Q 7
If a line is perpendicular to a radius at its end point on the circle, then that line is a tangent to the circle.
Q 8
A line perpendicular to a radius at some point inside the circle is always a tangent.
Q 9
Through a given point on a circle, exactly one tangent can be drawn.
Q 10
Through a point on a circle, infinitely many tangents can be drawn.
Q 11
From a point outside a circle, exactly two tangents can be drawn to the circle.
Q 12
From a point inside a circle, no tangent can be drawn to the circle.
Q 13
From a point on the circle, two tangents can be drawn to the circle.
Q 14
The two tangents drawn from an external point to a circle are always equal in length.
Q 15
If PA and PB are tangents from an external point P to a circle, then PA ? PB in general.
Q 16
The segment joining the centre of a circle to the midpoint of a chord is always perpendicular to that chord.
Q 17
The perpendicular from the centre of a circle to a chord always bisects the chord.
Q 18
If a line through the centre bisects a chord, it need not be perpendicular to the chord.
Q 19
The distance from the centre of a circle to a tangent is smaller than the radius of the circle.
Q 20
The perpendicular distance from the centre of a circle to a tangent equals the radius of the circle.
Q 21
If two circles touch each other externally, then the distance between their centres equals the sum of their radii.
Q 22
If two circles touch each other internally, the distance between their centres equals the difference of their radii.
Q 23
Every diameter of a circle is a chord of the circle.
Q 24
Every chord of a circle is a diameter of the circle.
Q 25
The angle between two tangents drawn from an external point to a circle is always the same, regardless of the location of the point.
Key Takeaways — CIRCLES
Core facts for CBSE Boards & exams
1
A tangent touches the circle at exactly ONE point (point of tangency).
2
Tangent ⊥ Radius at the point of contact — this is a theorem, always TRUE.
3
From an external point, the TWO tangent lengths to a circle are EQUAL.
4
A line can intersect a circle at 0 (non-intersecting), 1 (tangent), or 2 (secant) points.
5
The angle in a semicircle is 90° — angle subtended by diameter on the circle.
6
A chord is NOT a tangent; a secant passes THROUGH the circle at two points.