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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

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## Comments

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TopNewest60

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Its $\boxed{60}$

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60

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just a small correction a^2+b^2= 20^2

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Thnx edited.

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60

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60

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Ans underroot 140

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Only an integer answer is possible.

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60

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Let the diagonals meet at a point $E$, and let $EA=a, EB=b, EC=c, ED=d$

Applying PT, we get

$a^{2}+b^{2}=20^{2} \rightarrow Eq.1$

$b^{2}+c^{2}=70^{2} \rightarrow Eq.2$

$c^{2}+d^{2}=90^{2} \rightarrow Eq.3$

Eq.3 - Eq.2

$d^{2}-b^{2}=90^{2} -70^{2}\rightarrow Eq.4$

Eq.1 + Eq.4

$a^{2}+d^{2}=90^{2} -70^{2}+20^{2}$

$\Rightarrow a^{2}+d^{2}=3600=AD^{2}$

$\Rightarrow AD=60$

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60

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