Drawing tangents to a circle from a point on the circle

Q. The image of construction of two tangents inclined at ${60}^{\circ }$ drawn to a circle of radius of 4cm is given below.

Arrange the steps of construction the in correct order.
1.Take a point A on the circumerence of the circle and join OA. Draw a perpendicular to OA at point A.
2.Draw radius OC, making an angle of ${120}^{\circ }({180}^{\circ }-{60}^{\circ })$.
3.Draw a circle of radius 4cm and mark its centre as O.
4.Draw a perpendicular to OC at point C.Let both the perpendiculars intersect at point P. PA and PC are the required tangents inclined at an angle of ${60}^{\circ }$.

1. 1, 2, 3, 4
2. 1, 4, 3, 2
3. 3, 2, 1, 4
4. 3, 1, 2, 4

Q. Construct a circle of radius $2.5cm$. Take any point on the circle and draw a tangent to the circle at that point.
[3 Marks]

Q. The image of dividing line segment AB of length 12cm into 8cm and 4cm is given below.

Arrange the steps of construction in the correct order.
1. Mark three points on AX such that $A{A}_1=A_1{A}_2=A_2{A}_3$
2.Draw an acute angle $\angle BAX$
3.Join $A_3$ to B.
4.Draw $A_{2}C$ parallel to $A_{3}B$

1. 1, 2, 3, 4
2. 2, 1, 3, 4
3. 2, 3, 1, 4
4. 4, 2, 3, 1

Q.

For a tangent, the perpendicular line from the point of contact to the circle passes through the centre.

1. True

2. False

Q. In the figure below, two tangents are drawn from a point P to a circle meeting it at points A and C.
If $\angle AOC={120}^{\circ }$, what is the value of $\angle APC$?

1. ${120}^{\circ }$
2. ${30}^{\circ }$
3. ${60}^{\circ }$
4. ${80}^{\circ }$

Q. A circle of radius r has a centre O. What is first step to construct a tangent from a generic point P which is at a distance r from O?

1. Join OP.
2. With P as centre and radius > r, draw a circle and then join OP.
3. With P as centre and radius < r, draw a circle and then join OP.
4. With P as centre and radius = r, draw a circle and then join OP.

Q. The image of two tangents inclined at ${60}^{\circ }$ drawn to a circle of radius of 4cm is given below.
By which postulate is $\Delta AOP\cong \Delta COP$?

1. SSS
2. SAS
3. ASA
4. HL

Q.

A circle of radius r has a centre O. What is first step to construct a tangent from a generic point P which is at a distance r from O?

1. Join OP.

2. With P as centre and radius $<$ r, draw a circle and then join OP.

3. With P as centre and radius = r, draw a circle and then join OP.

4. With P as centre and radius $>$ r, draw a circle and then join OP.