The diagonals of the cyclic quadrilateral $$\(A B C D\)$$ intersect at $$\(X\)$$. Explain why triangle $$\(A D X\)$$ is similar to triangle $$\(B C X\)$$. Give a reason for each statement you make. ......................................................................................................................................... . ......................................................................................................................................... . ......................................................................................................................................... . .........................................................................................................................................

Mathematics
IGCSE&ALevel
CAIE
Exam No:0580_w20_qp_42 Year:2020 Question No:8(c)(i)

Answer:

angle \(A D X=\) angle \(B C X\) oe
same segment oe
angle \(D A X=\) angle \(C B X\) oe
same segment oe
angle \(A X D=B X C\) oe
[vertically] opposite oe
corresponding angles are equal oe

Knowledge points:

E4.7.10 angles in the same segment are equal
E4.7.2 angles at a point on a straight line and intersecting straight lines

Solution:

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