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Problem of the Day #64: Spider on a Triangle May 22, 2011

Posted by Seungln in : potd , trackback

Sreenath put a spider on triangle $ABC$ circumscribed by circle $O$, on which SeungIn is travelling.

Having seen the spider on vertex $A$, SeungIn, who is on vertex $B$, tries to maximize his distance from the spider. He is allowed to travel either on an arc of the circle or on an edge of the triangle.

Given that $AB$ = 13, $BC$ = 14, and $CA$ = 15, determine the maximum linear distance that SeungIn can attain from the spider.

Bonus: Now generalize this problem for any $ABC$.

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