Theorem 9 Two tangents drawn to a circle from the same point outside the circle are equal in length.
Proof :
Consider a circle, with centre
. Choose a point
outside the circle. Draw two tangents to the circle from point
, that meet the circle at
and
. Draw lines
,
and
.
The aim is to prove that
. In
and
,
(radii)
(
and
)
is common to both triangles.
(right angle, hypotenuse, side)
Circles v
Find the value of the unknown lengths.
Theorem 10 The angle between a tangent and a chord, drawn at the point of contact of the chord, is equal to the angle which the chord subtends in the alternate segment.
Proof :
Consider a circle, with centre
. Draw a chord
and a tangent
to the circle at point
. Chord
subtends angles at points
and
on the minor and major arcs, respectively.
Draw a diameter
and join
to
.
The aim is to prove that
and
. First prove that
as this result is needed to prove that
.
Circles vi
Find the values of the unknown letters.
Theorem 11 (Converse of
[link] ) If the angle formed between a line, that is drawn through the end point of a chord, and the chord, is equal to the angle subtended by the chord in the alternate segment, then the line is a tangent to the circle.
Proof :
Consider a circle, with centre
and chord
. Let line
pass through point
. Chord
subtends an angle at point
such that
.
The aim is to prove that
is a tangent to the circle. By contradiction. Assume that
is not a tangent to the circle and draw
such that
is a tangent to the circle.
If
is zero, then both
and
coincide and
is a tangent to the circle.
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,