TOPIC 6: CIRCLES
is a line which touches a circle. The point where the line touches the
circle is called the point of contact. A tangent is perpendicular to the
radius at the point of contact.
tangent to a circle is perpendicular to the radius at the point of
tangency. A common tangent is a line that is a tangent to each of two
circles. A common external tangent does not intersect the segment that
joins the centers of the circles. A common internal tangent intersects
the segment that joins the centers of the circles.
two chords intersect in a circle, the product of the lengths of the
segments of one chord equal the product of the segments of the other.
two secant segments are drawn to a circle from the same external point,
the product of the length of one secant segment and its external part
is equal to the product of the length of the other secant segment and
its external part.
a secant segment and tangent segment are drawn to a circle from the
same external point, the product of the length of the secant segment and
its external part equals the square of the length of the tangent
common tangents to a circle form a minor arc with a central angle of
140 degrees. Find the angle formed between the tangents.
TOPIC 7: THE EARTH AS THE SPHERE
P and Q are places west or east of each other, i.e they lie on the same
circle of latitude. Then when you travel due east or west from P to Q
you travel along an arc of the circle of latitude.
situation here is slightly different from that of the previous section.
While circles of longitude all have the same length, circles of
latitude get smaller as they get nearer the poles.
a ship is sailing in a sea current, or that a plane is flying in a
wind. Then the course set the ship or plane is not the direction that it
will move in. the actual direction and speed can be found either by
scale or by the use of Pythagoras’s theorem and trigonometry.
the line representing the motion of the ship relative to the water. At
the end of this line draw a line representing the current. Draw the
third side of the triangle. This side, shown with a double – headed
arrow, is the actual course of ship.
ship sets course due east. In still water the ship can sail at 15km/hr.
There is a current following due south of 4kkm/hr. use a scale drawing
- The speed of the ship
- The bearing of the sip.
one hour the ship sails 15km east relative to the water. Draw a
horizontal line of length 15cm. In one hour the current pulls the ship
4km south. At the end of the horizontal line, draw a vertical line of
- What course should be set?
- How long will the ship take to cover 120km?
With no current, the journey would take 8hrs. The journey takes
slightly longer when there is a current.Suppose a ship or a plane does
not directly reach a position. We can still find how close the ship or
plane is to the position.
small island is 200km away on a bearing of 075°. A ship sails on a
bearing of 070°.Find the closest that the ship is to the island.
5. Find thedistance in nau
MATHEMATICS FORM THREE OTHER TOPICS
FORM THREE MATHEMATICS STUDY NOTES TOPIC 1-2.
FORM THREE MATHEMATICS STUDY NOTES TOPIC 3-4.
FORM THREE MATHEMATICS STUDY NOTES TOPIC 5.
FORM THREE MATHEMTICS STUDY NOTES TOPIC 6-7.
FORM THREE MATHEMTICS STUDY NOTES TOPIC 8.
O’LEVEL MATHEMATICS NOTES
FORM ONE MATHEMATICS STUDY NOTES
FORM TWO MATHEMATICS STUDY NOTES
FORM THREE MATHEMATICS STUDY NOTES
FORM FOUR MATHEMATICS STUDY NOTES