CIRCLES
Frequently Asked Questions
A circle is the set of all points in a plane that are at a fixed distance from a fixed point called the centre.
The centre is the fixed point from which all points on the circle are equidistant.
The radius is the line segment joining the centre of the circle to any point on its circumference.
The diameter is a chord passing through the centre of the circle and is twice the radius.
A chord is a line segment joining any two points on the circumference of a circle.
The diameter is the longest chord of a circle.
A secant is a line that intersects a circle at two distinct points.
A tangent is a line that touches a circle at exactly one point.
The point where a tangent touches the circle is called the point of contact.
A tangent has exactly one common point with the circle.
A secant has exactly two common points with the circle.
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
The angle is always a right angle (90°).
Exactly one tangent can be drawn from a point on the circle.
No tangent can be drawn from a point inside the circle.
Two tangents can be drawn from a point outside the circle.
The lengths of tangents drawn from an external point to a circle are equal.
They form congruent right-angled triangles with equal radii and a common hypotenuse.
No, a tangent always lies outside the circle except at the point of contact.
It is the square of the length of the tangent drawn from the point to the circle.
The radius drawn to the point of contact is perpendicular to the tangent, not the chord.
No, a diameter always passes through the interior of the circle.
No, a chord is only the segment inside the circle, while a secant is the entire line.
No, but every secant contains a chord within the circle.
The chord formed becomes the diameter of the circle.
The angle between a tangent and a chord equals the angle in the opposite arc of the circle.
It is used to find angles formed by tangents and chords in a circle.
Right-angled triangles are formed with the radius perpendicular to the tangent.
The perpendicular distance from the centre to the tangent is the shortest.
Because the perpendicular gives the shortest distance from the centre to the tangent.
No, they meet at the external point and touch the circle at different points.
The internal segment lies inside the circle; the external segment lies outside.
Constructing tangents from an external point and at a point on the circle.
Yes, in wheels, circular tracks, mechanical parts, and optical instruments.
They help establish right angles, congruence, and length relationships.
Yes, tangents help analyze symmetry and rotational properties of circles.
The tangent–radius perpendicularity theorem.
Proofs, constructions, angle finding, and length-based problems.
Yes, especially based on equal tangents from an external point.
Because properties of tangents and secants are visual and diagram-dependent.
Yes, one tangent at each point on the circle.
It is the path traced by a point moving at a constant distance from a fixed point.
It connects geometry, constructions, and logical proofs.
No, conceptual clarity and diagram understanding are essential.
Learn theorems, practice diagrams, and write step-wise proofs clearly.
