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Triangle A B C with A B=13 ,B C=5, and A...

Triangle `A B C` with `A B=13 ,B C=5,` and `A C=12` slides on the coordinates axes with `Aa n dB` on the positive x-axis and positive y-axis respectively. The locus of vertex `C` is a line `12 x-k y=0.` Then the value of `k` is_____________

Text Solution

Verified by Experts


`"Since " angleBCA = 90^(@),` points A, O, B, C are concyclic.
`"Let "angleAOC = theta.`
`angleBOC = angleBAC`
`"tan"((pi)/(2)-theta) = (5)/(12)`
`(x)/(y) = (5)/(12) " or " 12-5y=0`
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