9.2 CHAPTER 9. GEOMETRY
�A
B
O
P
Consider a circle, with centre O. Choose a point P outside the circle. Drawtwo tangents to the circle
from point P , that meet the circle at A and B. Draw lines OA, OB and OP.
The aim is to prove that AP = BP.
In�OAP and�OBP ,
- OA = OB (radii)
2.∠OAP =∠OBP = 90◦(OA⊥ AP and OB⊥ BP )- OP is common to both triangles.
�OAP≡�OBP (right angle, hypotenuse, side)
∴ AP = BP
Exercise 9 - 5
Find the value of the unknown lengths.