11 x1 t13 06 tangent theorems 2
TRANSCRIPT
Alternate Segment
Theorem
Alternate Segment
Theorem (9) An angle formed by a tangent to a circle with a chord drawn to the
point of contact is equal to any angle in the alternate segment.
Alternate Segment
Theorem (9) An angle formed by a tangent to a circle with a chord drawn to the
point of contact is equal to any angle in the alternate segment.
O
X P
A B
Alternate Segment
Theorem (9) An angle formed by a tangent to a circle with a chord drawn to the
point of contact is equal to any angle in the alternate segment.
alternate segment theoremBPX PAB
O
X P
A B
Alternate Segment
Theorem (9) An angle formed by a tangent to a circle with a chord drawn to the
point of contact is equal to any angle in the alternate segment.
alternate segment theoremBPX PAB
O
X P
A B
ABPAPY :Prove
Y
Alternate Segment
Theorem (9) An angle formed by a tangent to a circle with a chord drawn to the
point of contact is equal to any angle in the alternate segment.
alternate segment theoremBPX PAB
O
X P
A B
ABPAPY :Prove
Proof: Join PO and produce to meet the
circumference at Z
Z
Y
Alternate Segment
Theorem (9) An angle formed by a tangent to a circle with a chord drawn to the
point of contact is equal to any angle in the alternate segment.
alternate segment theoremBPX PAB
O
X P
A B
ABPAPY :Prove
Proof: Join PO and produce to meet the
circumference at Z Join AZ
Z
Y
Alternate Segment
Theorem (9) An angle formed by a tangent to a circle with a chord drawn to the
point of contact is equal to any angle in the alternate segment.
alternate segment theoremBPX PAB
O
X P
A B
ABPAPY :Prove
Proof: Join PO and produce to meet the
circumference at Z Join AZ
Z
tangentradius 90 ZPY
Y
Alternate Segment
Theorem (9) An angle formed by a tangent to a circle with a chord drawn to the
point of contact is equal to any angle in the alternate segment.
alternate segment theoremBPX PAB
O
X P
A B
ABPAPY :Prove
Proof: Join PO and produce to meet the
circumference at Z Join AZ
Z
tangentradius 90 ZPY
Y -90 APYAPZ
Alternate Segment
Theorem (9) An angle formed by a tangent to a circle with a chord drawn to the
point of contact is equal to any angle in the alternate segment.
alternate segment theoremBPX PAB
O
X P
A B
ABPAPY :Prove
Proof: Join PO and produce to meet the
circumference at Z Join AZ
Z
tangentradius 90 ZPY
Y -90 APYAPZ
semicirclein 90 PAZ
O
X P
A B
Z
Y
O
X P
A B
Z
Y
sum 180 APZAPZAZPPAZ
O
X P
A B
Z
Y
sum 180 APZAPZAZPPAZ
1809090 APYAZP
O
X P
A B
Z
Y
sum 180 APZAPZAZPPAZ
1809090 APYAZP
APYAZP
O
X P
A B
Z
Y
sum 180 APZAPZAZPPAZ
1809090 APYAZP
APYAZP
's in same segment =AZP ABP
O
X P
A B
Z
Y
sum 180 APZAPZAZPPAZ
1809090 APYAZP
APYAZP
's in same segment =AZP ABP
ABPAPY
O
X P
A B
Z
Y
sum 180 APZAPZAZPPAZ
1809090 APYAZP
APYAZP
's in same segment =AZP ABP
ABPAPY
Exercise 9F; 2ace etc, 3bd, 4bd, 5b, 7b, 9b, 10b, 12, 14, 15b