Common Sense On A Graph

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There are 3 functions a graph. ${y}= (({{k}/2})^2-{(x-{k}/2)}^2)^{1/2}$ , ${y}={k}$ , and ${x}={k}$ .There is a point of intersection between the first two functions ${P}$ .There are several tangential lines that include both a point on the first curve and P.Find the average length of these lines when k = 100.

The answer is 100.

1 solution

Aaryan Vaishya
Oct 19, 2019

Since the first function is clearly a circle of of radius k/2 and center k/2,0,and the two other functions form a square of side length k, the length of the tangent from P to k,0 is k.By the two tangent theorem the rest of the tangents are also length k.Therefore the average length is k=100.

Common Sense On A Graph

The answer is 100.

1 solution

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