Tangent Theorems
11X1 T07 05 tangent theorems 1
Dec 03, 2014
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Tangent Theorems
Tangent Theorems(7) Assumption:
The size of the angle between a tangent and the radius drawn to the point of contact is 90 degrees.
Tangent Theorems(7) Assumption:
The size of the angle between a tangent and the radius drawn to the point of contact is 90 degrees.
tangentradius XYOX
Tangent Theorems(7) Assumption:
The size of the angle between a tangent and the radius drawn to the point of contact is 90 degrees.
tangentradius XYOX
Let x be the distance of the chord from the centre.
xO X
Y
Z
Tangent Theorems(7) Assumption:
The size of the angle between a tangent and the radius drawn to the point of contact is 90 degrees.
tangentradius XYOX
Let x be the distance of the chord from the centre.
y
xLet 2y be the length of the chord.
y
O X
Y
Z
Tangent Theorems(7) Assumption:
The size of the angle between a tangent and the radius drawn to the point of contact is 90 degrees.
tangentradius XYOX
Let x be the distance of the chord from the centre.
y
xLet 2y be the length of the chord.
y
O X
Y
Z
chord tomidpoint,
tocentre joining line YZOX
Tangent Theorems(7) Assumption:
The size of the angle between a tangent and the radius drawn to the point of contact is 90 degrees.
tangentradius XYOX
Let x be the distance of the chord from the centre.
y
xLet 2y be the length of the chord.
y
O X
Y
Z
chord tomidpoint,
tocentre joining line YZOX
0y
radius As
x
Tangent Theorems(7) Assumption:
The size of the angle between a tangent and the radius drawn to the point of contact is 90 degrees.
tangentradius XYOX
Let x be the distance of the chord from the centre.
y
O xLet 2y be the length of the chord.
y
X
Y
Z
chord tomidpoint,
tocentre joining line YZOX
0y
radius As
x
Tangent Theorems(7) Assumption:
The size of the angle between a tangent and the radius drawn to the point of contact is 90 degrees.
tangentradius XYOX
Let x be the distance of the chord from the centre.
yO x
Let 2y be the length of the chord.
yX
Y
Z
chord tomidpoint,
tocentre joining line YZOX
0y
radius As
x
Tangent Theorems(7) Assumption:
The size of the angle between a tangent and the radius drawn to the point of contact is 90 degrees.
tangentradius XYOX
Let x be the distance of the chord from the centre.
O xLet 2y be the length of the chord.
X
Y
Z
chord tomidpoint,
tocentre joining line YZOX
0y
radius As
x
(8) From any external point, two equal tangents may be drawn to a circle. The line joining this point to the centre is an axis of symmetry
(8) From any external point, two equal tangents may be drawn to a circle. The line joining this point to the centre is an axis of symmetry
A
B
O T
(8) From any external point, two equal tangents may be drawn to a circle. The line joining this point to the centre is an axis of symmetry
arepoint external from tangents BTAT
A
B
O T
(8) From any external point, two equal tangents may be drawn to a circle. The line joining this point to the centre is an axis of symmetry
arepoint external from tangents BTAT
A
B
O T
BTAT :Prove
(8) From any external point, two equal tangents may be drawn to a circle. The line joining this point to the centre is an axis of symmetry
arepoint external from tangents BTAT
A
B
O T
BTAT :Prove
Proof: Join OA, OB and OT
(8) From any external point, two equal tangents may be drawn to a circle. The line joining this point to the centre is an axis of symmetry
arepoint external from tangents BTAT
A
B
O T
BTAT :Prove
Proof: Join OA, OB and OT
tangentradius 90 OBTOAT
(8) From any external point, two equal tangents may be drawn to a circle. The line joining this point to the centre is an axis of symmetry
arepoint external from tangents BTAT
A
B
O T
BTAT :Prove
Proof: Join OA, OB and OT
tangentradius 90 OBTOAT
OT is a common side
(8) From any external point, two equal tangents may be drawn to a circle. The line joining this point to the centre is an axis of symmetry
arepoint external from tangents BTAT
A
B
O T
BTAT :Prove
Proof: Join OA, OB and OT
tangentradius 90 OBTOAT
radii OBOA
OT is a common side
(8) From any external point, two equal tangents may be drawn to a circle. The line joining this point to the centre is an axis of symmetry
arepoint external from tangents BTAT
A
B
O T
BTAT :Prove
Proof: Join OA, OB and OT
tangentradius 90 OBTOAT
radii OBOA
OT is a common side
RHSOBTOAT
(8) From any external point, two equal tangents may be drawn to a circle. The line joining this point to the centre is an axis of symmetry
arepoint external from tangents BTAT
A
B
O T
BTAT :Prove
Proof: Join OA, OB and OT
tangentradius 90 OBTOAT
radii OBOA
OT is a common side
RHSOBTOAT matching sides in 'sAT BT
H
O T
collineargent common tan of
contact ofpoint and centres collinear is OTH
H
O T
collineargent common tan of
contact ofpoint and centres collinear is OTH
H
O T
Exercise 9E; 1aceg, 2bdfh, 3ac, 4bd, 6bc, 9, 10ac, 12b, 14, 16a
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