MHB A,B,C,D cocyclic prove AC^2=AB×AD+BC^2

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In the discussion about the cyclic quadrilateral ABCD with the condition BC = CD, the goal is to prove the equation AC² = AB × AD + BC². Participants explore geometric properties and relationships inherent in cyclic quadrilaterals, utilizing the Law of Cosines and properties of angles subtended by the same arc. The hint suggests leveraging these properties to establish the necessary relationships between the sides and diagonals. The proof ultimately relies on the equality of angles and the application of trigonometric identities. The conclusion reinforces the validity of the equation within the context of cyclic quadrilaterals.
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$ABCD$ is a Cyclic quadrilateral,given $BC=CD$

Prove:

$AC^2=AB\times AD+BC^2$
 
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Albert said:
$ABCD$ is a Cyclic quadrilateral,given $BC=CD$

Prove:

$AC^2=AB\times AD+BC^2$
hint:
using the following diagram:
View attachment 6569
 

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