E-DM04 · A moving vertex and a fixed area
\(A=(0,0)\), \(B=(10,0)\), \(C=(t,4)\), where t is real.
Find the area of triangle ABC and explain why it does not depend on t.
Find all t for which \(AC^2+BC^2=100\).
For these positions, justify that the angle at C is a right angle and find the exact perimeter.
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