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Albert1
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$ABCD$ is a Cyclic quadrilateral,given $BC=CD$
Prove:
$AC^2=AB\times AD+BC^2$
Prove:
$AC^2=AB\times AD+BC^2$
MHB A,B,C,D cocyclic prove AC^2=AB×AD+BC^2
- Thread starter Albert1
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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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Albert1
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Obviously, there is something elementary I am missing here.
To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix
in the real plane; taking the transpose we get
which then corresponds to a-bi...
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