11. Tangents to Circles
(a) How to memorize the tangent properties?
If PA and PB are tangents from P to the circle
at points A and B respectively:
∠AOP =∠BOP
∠APO =∠BPO

PA = PB
A
tangent
properties
O
P
Tangent properties Easy Memory Tips:
B
AAS
△APO  △BPO (AAS)
i.e. the corresponding angles in the two triangles are equal:
∠AOP =∠BOP
∠APO =∠BPO
and the corresponding sides of the two triangles are equal:

PA = PB
11. Tangents to Circles
(b) How to memorize the angle in the alternate segment?
The angle between the
The opposite angle
=
from the chord
tangent and the chord
B
Angle in Alternate Segment
Easy Memory Tips:
C
Use a torch to light up chord AC from B,
then use another torch to light up chord
AC from A.
We can find an overlapping region which
the two torches lighted up.
P
The overlapping region is exactly the corresponding
positions of ‘∠ in alt. segment’.
A
Q