Tangent to a Circle
Tangent to a Circle: Overview
This Topic covers sub-topics such as Tangent to a Circle, Parallel Tangents to a Circle, Point of Contact of a Tangent to a Circle and, Property Related to Tangent and Radius of a Circle
Important Questions on Tangent to a Circle
In Fig., from an external point , two tangents and are drawn to a circle with centre and radius . If , show that.

In the given figure, is centre of the circle. The radius of the circle is and is tangent drawn to the circle from point . If and , then find the value of

In the above figure, seg AB and seg AD are tangent segments drawn to a circle with centre C from exterior point A, then prove that

In figure, the radius is . is a square, find the length of .


The line is a tangent to the circle at the point . The circle is centred at the origin.
Check if the line passes through the point .

Shown below is a circle and a square. The circle with centre has a radius of .
Find the area of the shaded region. Show your work and give valid reasons. (Note: If needed, take as )

In the figure below, and are the centres of two semi-circles having radii and respectively. is a common tangent.
Find the length of PQ. Draw a rough figure, show your work and give valid reasons.

Shown below is a circle with centre . is a tangent to the circle.
Find the measure of . Show your work and give valid reasons.

In the given figure find the value of if the length of cm. Given that the radius of inner and the outer circle are


In the figure given below, AB is a tangent to the circle with centre O.

The radii of two concentric circles are . If a chord of a larger circle touches the smaller circle then the length of the chord is _______

In the adjoining fig PA and PB are tangents drawn from an external point P to a circle with centre O. Then prove that

In the given figure, is the centre of the circle, is tangent to the circle at . If . Find and .

In the given figure, is a diameter of a circle with centre and is a tangent at . is a point on the circle such that produced intersects the tangent at and . Find .

In the given figure, is a tangent and is a secant. If and , then find the length of .

In the given figure, and are tangents to the circle centre , at and , respectively,
Find the value of .

The diagram shows a circle , centre . The line is a tangent to the circle. Calculate angle .

In a park, four poles are standing at positions and around the fountain such that the cloth joining the poles and touches the fountain at and respectively as shown in figure:
Based on the above information, answer the following question:
If is the centre of the circular fountain, then
