circle geometry help 5

Jun 2009
806
275
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
ABCD is cyclic quadrilateral. So

\(\displaystyle \angle{CAB}=\angle{CDB} \)

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 \(\displaystyle \angle(ACF) = \angle(DBF) = 90 degrees.\)
 
May 2010
39
0
ABCD is cyclic quadrilateral. So

\(\displaystyle \angle{CAB}=\angle{CDB} \)

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.
 
Jun 2009
806
275
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.
 
May 2010
39
0
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