# circle geometry help 5

#### sa-ri-ga-ma

http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2004exams/pdf_doc/maths_ext1_04.pdf

can somebody help me with question 6a with explanations and reasons thanks in advance

$$\displaystyle \angle{CAB}=\angle{CDB}$$

In triangle ACF and DBF,

$$\displaystyle \angle(AFC) + \angle(ACF) + \angle(CAF) = 180 degrees$$

$$\displaystyle \angle(BFC) + \angle(DBF) + \angle(BDF) = 180 degrees$$

Therefore $$\displaystyle \angle(ACF) = \angle(DBF)$$

Since EBFC is cyclic quadrilateral, $$\displaystyle \angle(ACF) + \angle(DBF) = 180 degrees$$

SO $$\displaystyle \angle(ACF) = \angle(DBF) = 90 degrees.$$

#### andy69

$$\displaystyle \angle{CAB}=\angle{CDB}$$

In triangle ACF and DBF,

$$\displaystyle \angle(AFC) + \angle(ACF) + \angle(CAF) = 180 degrees$$

$$\displaystyle \angle(BFC) + \angle(DBF) + \angle(BDF) = 180 degrees$$

Therefore $$\displaystyle \angle(ACF) = \angle(DBF)$$

Since EBFC is cyclic quadrilateral, $$\displaystyle \angle(ACF) + \angle(DBF) = 180 degrees$$

SO $$\displaystyle \angle(ACF) = \angle(DBF) = 90 degrees.$$
hey thanks for the help do you know how to do part 2 of that question im not sure what it means here is the question (ii) Find an expression for the length of AD in terms of r.

#### sa-ri-ga-ma

hey thanks for the help do you know how to do part 2 of that question im not sure what it means here is the question (ii) Find an expression for the length of AD in terms of r.
In all five posts I have observed that you are not putting your efforts.
For example in the above problem I have shown that angle DBF = 90 degrees. Then what is the angle DBA? The answer to this question leads to the length of AD.

#### andy69

In all five posts I have observed that you are not putting your efforts.
For example in the above problem I have shown that angle DBF = 90 degrees. Then what is the angle DBA? The answer to this question leads to the length of AD.
ok sorry ill put 100% effort from now on

#### sa-ri-ga-ma

ok sorry ill put 100% effort from now on
ABF is a straight line. Angle DBF = 90 degrees. Then angle DBA = .....?

#### andy69

ABF is a straight line. Angle DBF = 90 degrees. Then angle DBA = .....?
90 degrees because angle DBA is apart of ABF the straight line.

#### sa-ri-ga-ma

90 degrees because angle DBA is apart of ABF the straight line.
Yes. Now ABD is a right angled triangle in a circle. It is possible only when AD is ........

#### andy69

Yes. Now ABD is a right angled triangle in a circle. It is possible only when AD is ........