\(A,B,C,D\) and \(E\) lie on the circle.
\(AC\) and \(BD\) intersect at \(X\).
Angle \(ACD=55^\circ\) and angle \(CXD=88^\circ\).
Complete the statements, giving a geometrical reason in each part.
Angle \(CDB=\) ............ because ........................................
Angle \(ABD=\) ............ because ........................................
Angle \(AED=\) ............ because ........................................[6]
Triangle \(CXD\) is mathematically similar to triangle \(BXA\).
\(DX=8.0\text{ cm},\ BX=2.7\text{ cm}\) and \(AX=4.0\text{ cm}\).
Work out the length of \(CX\).[2]
Complete the statement.
Area of triangle \(CXD\) : area of triangle \(BXA=\) ............ : ............[1]