Engineering
Mathematics
A Circle
Question
A circular table is pushed into a corner in a rectangular room so that it touches both walls. A point on the edge of the table between the two points of contact on the smaller arc, is 2 units from one wall and 9 units from the other wall. The radius of the circular table is
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Solution
Equation of the circle is (x – r)2 + (y – r)2 = r2
x2 + y2 – 2xr – 2yr + r2 = 0 .....(1)
point (2, 9) must satisfy (1)
hence r2 – 22r + 85 = 0
(r – 17)(r – 5) = 0
⟹ r = 17 Ans. (r = 5 not possible)]
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