List of top Mathematics Questions on Tangent to a Circle

In the above figure tangents \(PA\) and \(PB\) from a point \(P\) to a circle with centre \(O\) are inclined to each other at an angle of \(60^\circ\), then \(\angle POA =\) _____.
A circle can have _____ parallel tangents at the most.
The lengths of the two tangents from an external point to a circle are _____.
The length of tangent from a point 17 cm away from the centre of a circle of radius 8 cm is _____ cm.
From an external point $P$, two tangents $PA$ and $PB$ are drawn to a circle with centre $O$. At a point $E$ on the circle, a tangent is drawn which intersects $PA$ and $PB$ at $C$ and $D$ respectively. If $PA = 10$ cm, find the perimeter of $\triangle PCD$.
In the given figure, two tangents PT and QT are drawn to a circle with centre O from an external point T. Prove that \(\angle\) PQT = \(2\angle\) OPQ.
Problem Figure
In two concentric circles, the radii \(OA = r\) cm and \(OQ = 6\) cm, as shown in the figure. Chord $CD$ of the larger circle is a tangent to the smaller circle at $Q$. $PA$ is tangent to the larger circle. If $PA$ = $16$ cm and $OP = 20$ cm, find the length of $CD$.
Problem Figure
Problem Figure
Assertion (A): If the PA and PB are tangents drawn to a circle with center O from an external point P, then the quadrilateral OAPB is a cyclic quadrilateral.
Reason (R): In a cyclic quadrilateral, opposite angles are equal.
From an external point $P$, two tangents $PA$ and $PB$ are drawn to a circle with centre $O$. At a point $E$ on the circle, a tangent is drawn which intersects $PA$ and $PB$ at $C$ and $D$ respectively. If $PA = 10$ cm, find the perimeter of $\triangle PCD$.
In the given figure, two tangents PT and QT are drawn to a circle with centre O from an external point T. Prove that \(\angle\) PQT = \(2\angle\) OPQ.
Problem Figure
In two concentric circles, the radii \(OA = r\) cm and \(OQ = 6\) cm, as shown in the figure. Chord $CD$ of the larger circle is a tangent to the smaller circle at $Q$. $PA$ is tangent to the larger circle. If $PA$ = $16$ cm and $OP = 20$ cm, find the length of $CD$.
Problem Figure
Problem Figure
Assertion (A): If the PA and PB are tangents drawn to a circle with center O from an external point P, then the quadrilateral OAPB is a cyclic quadrilateral.
Reason (R): In a cyclic quadrilateral, opposite angles are equal.
A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see Fig. 10.14). Find the sides AB and AC.
A triangle ABC is circumscribed a circle of radius 4 cm
Fig. 10.14
Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
Fill in the blanks :
  1. A tangent to a circle intersects it in ____ point(s).
  2. A line intersecting a circle in two points is called a ____ .
  3. A circle can have ____ parallel tangents at the most.
  4. The common point of a tangent to a circle and the circle is called ____ .
How many tangents can a circle have?