1. Tangents to a Circle

2. AB = tangent to the circle
Tangents to A Circle
A tangent to a circle
- a straight line which touches the circle at only one point
- perpendicular to the radius at the point of contact A B
AB = tangent to the circle

3. Constructing tangents to a circle
The diagram below shows a circle with centre O.
Construct the tangent to the circle at the point P. P O

4. Constructing tangents to a circle
Solution:
Step 1:
Draw a straight line joining point P and centre O. P O

5. Constructing tangents to a circle
Solution:
Step 2:
Adjust your compasses so that its radius is slightly more than half of the length of OP. P O

6. Constructing tangents to a circle
Solution:
Step 3:
Place your compasses at P. On the line OP, draw one point on both sides of P. P O

7. Constructing tangents to a circle
Solution:
Step 4:
Place your compasses at one of the point on the line OP, draw an arc above and below the line OP. P O

8. Constructing tangents to a circle
Solution:
Step 5:
With the same radius and another point on line OP as centre, draw another two arcs to intersect the ones drawn in step 4. P O

9. Constructing tangents to a circle
Solution:
Step 6:
Tangent at P
Join the two intersections with a straight line. P O

10. Constructing tangents to a circle
The diagram below shows a circle with centre O.
Construct two tangents to the circle that pass through the point T. T O

11. Constructing tangents to a circle
Solution:
Step 1:
Draw a straight line joining point T and centre O. T O O

12. Constructing tangents to a circle
Solution:
Step 2:
Adjust your compasses so that its radius is slightly more than half of the length of OT. T O

13. Constructing tangents to a circle
Solution:
Step 3:
Place your compasses at T. Draw a short arc above and below the line OT. T O

14. Constructing tangents to a circle
Solution:
Step 4:
With the same radius and your compasses placed at O, draw arcs to intersect the ones drawn in Step 3. T O

15. Constructing tangents to a circle
Solution:
Step 5:
Join the two intersections with a straight line. T O

16. Constructing tangents to a circle
Solution:
Step 6:
Label the midpoint as M. Using M as the centre and OM as the radius, draw two arcs that cut the circle at P and Q. P T O M Q

17. Tangents to A Circle Constructing tangents to a circle Solution:
Step 7:
Join points P and Q to point T. P
Lines PT and QT are tangents to the circle that pass through point T T O M Q

18. Properties related to two tangents to a circleQ y° x°
PT = QT
 PTO =  OTQ
 POT =  QOT
∆POT and ∆QOT are congruent.

19. The End