Everything Maths Grade 12

9.2 CHAPTER 9. GEOMETRY

Example 2: Circle Geometry II

QUESTION

A

B

C

D

E

F

G H

FD is drawn parallel to thetangent CB

Prove that:

1. FADE is cyclic

2.�AFE///�CBD

3.FCGH×AG=DCBD×FE

SOLUTION

Step 1 : In this case, the best way to show FADE is a cyclic quadrilateral is to look for

equal angles, subtendedby the same chord.

Let∠BCD = x

∴∠CAH = x (∠ between tangent BC and chord CE)

∴∠FDC = x (alternate∠, FD� CB)

∴ FADE is a cyclic quadrilateral(chord FE subtends equal∠’s)

Step 2 : To show these 2 triangles similar we will need3 equal angles. We canuse the

result from the previousquestion.