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In cyclic quadrilateral $ABCD$ consider $DD_1 ⊥ DC$ with $D_1$ on line $AB$, $BB_1 ⊥ AB$ with $B_1$ on line $DC$. Prove that $AC ∥ B_1D_1$.

I'm having trouble drawing this cyclic quadrilateral. At first, I put $D_1$ at the intersection of $AB$ and $DA$ and $B_1$ at the intersection of $DC$ and $BC$. But such placements for $D_1$ and $B_1$ made $AC$ the exact same line as $B_1D_1$. So that didn't work. Now I guessing and testing to no avail.

Peter Woolfitt
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Love Light
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1 Answers1

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The idea is that the intersections don't have to occur inside the circle. The question has $D_1$ on line $AB$ and $B_1$ on line $DC$. Here's a picture that can hopefully sort things out.

circle woo

Peter Woolfitt
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