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

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SUMMARY

The discussion focuses on proving the equation \( AC^2 = AB \times AD + BC^2 \) for cyclic quadrilateral \( ABCD \) where \( BC = CD \). The proof utilizes properties of cyclic quadrilaterals and the Ptolemy's theorem. Participants emphasize the importance of understanding the relationships between the sides and diagonals in cyclic figures to derive the required equation effectively.

PREREQUISITES
  • Cyclic quadrilateral properties
  • Ptolemy's theorem
  • Basic geometric proofs
  • Understanding of triangle properties
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  • Explore geometric proof techniques for quadrilaterals
  • Investigate the relationship between diagonals and sides in cyclic figures
  • Learn about the properties of isosceles triangles in cyclic quadrilaterals
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Mathematics students, geometry enthusiasts, and educators looking to deepen their understanding of cyclic quadrilaterals and their properties.

Albert1
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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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