max <ABC wanted, A,C on same diameter (2003-04 Savin Competition 6-8 p8)

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max <ABC wanted, A,C on same diameter (2003-04 Savin Competition 6-8 p8)

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#1 h Jun 10, 2021, 6:09 PM • 1 Y

Y by Mango247

A circle is given, inside which points $A$ and $C$ are marked, lying on the same diameter. Using a compass and a ruler without divisions, construct on the circle a point $B$ for which the value of the angle $ABC$ is the greatest possible.

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#2 h Jun 10, 2021, 6:12 PM

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The maximum value of $\angle ABC$ is $90^{\circ}$ , with equality at any point other than $A,C$ , so just pick a point on the circle.

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#3 h Jun 10, 2021, 6:17 PM

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points $A,C$ are not endpoints of the diameter

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