Tangent as a Special Case of Secant

Q.

The length of the tangent drawn to a circle with radius $7cm$ from a point $25cm$ away from the centre is ___ $cm.$

Q.

Consider the following statements and choose the correct option.
1) A tangent is a line that touches the circle at one point.
2) A tangent is an extreme case of the secant where the points of intersection coincide.

1. 1 is true and 2 is false.

2. 1 is false and 2 is true.

3. Both 1 and 2 are true.

4. Both 1 and 2 are false.

Q. Find angle PTQ in the figure.

1. 70 degrees
2. 65 degrees
3. 35 degrees
4. 110 degrees

Q.

Under which condition can a secant to a circle be called a tangent?

1. The points of intersection are infinite distance apart.

2. The secant passes through the centre of the circle.

3. The points of intersection are coincident.

4. The secant is a curved line.

Q.

Consider the following statements and choose the correct option.
1) A tangent is a line that touches the circle at one point.
2) A tangent is an extreme case of the secant where the points of intersection coincide.

1. 1 is true and 2 is false.

2. 1 is false and 2 is true.

3. Both 1 and 2 are true.

4. Both 1 and 2 are false.

Q. From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that Δ APB is equilateral.

Q.

Let a line meet a circle at A and B. This line is rotated about point A in clockwise direction such that B always remains on the circumference of the circle until point B coincides with A. What is the resulting line called?

1. Chord

2. Secant

3. Tangent

4. No term

Q.

Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 6 cm respectively, as shown in the figure. If AP = 6 cm then find the length of BP.

1. 8 cm

2. 16 cm

3. 10 cm

4. 6 cm

Q.

A tangent to a circle is a line that intersects the circle at only ________.

1. one point
2. two points

Q.

Let a line meet a circle at A and B. This line is rotated about point A in clockwise direction such that B always remains on the circumference of the circle until point B coincides with A. What is the resulting line called?

1. Secant

2. Chord

3. Tangent

4. No term

Q.

Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 6 cm respectively, as shown in the figure. If AP = 6 cm then find the length of BP.

1. 8 cm

2. 16 cm

3. 10 cm

4. 6 cm

Q.

ABC is a right angled triangle with AB = 12 cm and AC = 13 cm. A circle, with centre O, has been inscribed inside the triangle.

Calculate the value of x, the radius of the inscribed circle.

1. 8 cm

2. 3 cm

3. 2 cm

4. 9 cm

Q.

In the given figure, O is the centre of the circle. Find the value of $X$.

1. ${30}^{\circ }$

2. ${50}^{\circ }$

3. ${40}^{\circ }$

4. ${100}^{\circ }$

Q.

Under which condition can a secant to a circle be called a tangent?

1. The points of intersection are infinite distance apart.

2. The secant passes through the centre of the circle.

3. The points of intersection are coincident.

4. The secant is a curved line.

Q. is a line that touches a circle at only one point, and is a line that intersects a circle at two distinct points.

1. Arc
2. Tangent
3. secant
4. sector

Q.

In the given figure, O is the centre of the circle. Find the value of $X$.

1. ${30}^{\circ }$

2. ${40}^{\circ }$

3. ${50}^{\circ }$

4. ${100}^{\circ }$

Q. Chord of a circle is always bisected by the radius of that circle.

1. False
2. True

Q.

From the figure, name

(a) Tangents drawn from A to circle C₁.

(b) Tangents drawn from A to circle C₂.

(c) Tangents drawn from B to circles C₁ and C₂.

(d) Sets of equal tangents.

Q.
If $\angle BCD={50}^{\circ },$ then $\angle BAD$ = ___.

1. ${50}^{\circ }$
2. ${100}^{\circ }$
3. ${70}^{\circ }$
4. ${25}^{\circ }$

Q. ______ is a line that touches a circle at only one point, and ______ is a line that intersects a circle at two distinct points.

1. Tangent, secant
2. Secant, secant
3. Tangent, tangent
4. Secant, tangent

Q.

Under which condition can a secant to a circle be called a tangent?

1. The secant passes through the centre of the circle.

2. The points of intersection are infinite distance apart.

3. The points of intersection are coincident.

4. The secant is a curved line.

Q.

From the figure, name

(a) Tangents drawn from A to circle C₁.

(b) Tangents drawn from A to circle C₂.

(c) Tangents drawn from B to circles C₁ and C₂.

(d) Sets of equal tangents.