Embed Size (px)
DESCRIPTION
Tangents to a Circle. A tangent to a circle. A. B. Tangents to A Circle. - a straight line which touches the circle at only one point. - perpendicular to the radius at the point of contact. AB = tangent to the circle. Constructing tangents to a circle. - PowerPoint PPT Presentation
Citation preview
Pearson Malaysia Sdn Bhd
Form 4 Chapter 8: Circles III
Pearson Malaysia Sdn Bhd
A tangent to a circle
- a straight line which touches the circle at only one point
A B
AB = tangent to the circle
- perpendicular to the radius at the point of contact
Pearson Malaysia Sdn Bhd
Constructing tangents to a circle
The diagram below shows a circle with centre O.Construct the tangent to the circle at the point P.
O
P
Pearson Malaysia Sdn Bhd
O
P
Solution:
Draw a straight line joining point P and centre O.
Step 1:
Constructing tangents to a circle
Pearson Malaysia Sdn Bhd
O
P
Solution:
Step 2:
Adjust your compasses so that its radius is slightly more than half of the length of OP.
Constructing tangents to a circle
Pearson Malaysia Sdn Bhd
O
P
Solution:
Place your compasses at P. On the line OP, draw one point on both sides of P.
Step 3:
Constructing tangents to a circle
Pearson Malaysia Sdn Bhd
O
P
Solution:
Place your compasses at one of the point on the line OP, draw an arc above and below the line OP.
Step 4:
Constructing tangents to a circle
Pearson Malaysia Sdn Bhd
O
P
Solution:
With the same radius and another point on line OP as centre, draw another two arcs to intersect the ones drawn in step 4.
Step 5:
Constructing tangents to a circle
Pearson Malaysia Sdn Bhd
O
P
Solution:
Join the two intersections with a straight line.
Step 6:
Tangent at P
Constructing tangents to a circle
Pearson Malaysia Sdn Bhd
The diagram below shows a circle with centre O.Construct two tangents to the circle that pass through the point T.
Constructing tangents to a circle
OT
Pearson Malaysia Sdn Bhd
OT
Solution:
Step 1:
Draw a straight line joining point T and centre O.
Constructing tangents to a circle
O
Pearson Malaysia Sdn Bhd
OT
Solution:
Step 2:
Adjust your compasses so that its radius is slightly more than half of the length of OT.
Constructing tangents to a circle
Pearson Malaysia Sdn Bhd
OT
Solution:
Step 3:Place your compasses at T. Draw a short arc above and below the line OT.
Constructing tangents to a circle
Pearson Malaysia Sdn Bhd
OT
Solution:
With the same radius and your compasses placed at O, draw arcs to intersect the ones drawn in Step 3.
Step 4:
Constructing tangents to a circle
Pearson Malaysia Sdn Bhd
OT
Solution:
Step 5:
Join the two intersections with a straight line.
Constructing tangents to a circle
Pearson Malaysia Sdn Bhd
OT
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.
M
P
Q
Constructing tangents to a circle
Pearson Malaysia Sdn Bhd
OT
Solution:
Step 7:
Join points P and Q to point T.
M
P
Q
Lines PT and QT are tangents to the
circle that pass through point T
Constructing tangents to a circle
Pearson Malaysia Sdn Bhd
Properties related to two tangents to a circle
OT
P
Q
y°
y°
x°x°
PT = QT
PTO = OTQ
POT = QOT
∆POT and ∆QOT are congruent.
Pearson Malaysia Sdn Bhd
