A BC D is a rectangle. A circle through C touches A B and A D at M , N , respectively. If the rectangle has area K 2 ( K 0 ) , find the perpendicular distance from C to MN .

Question

A BC D is a rectangle. A circle through C touches A B and A D at M , N , respectively. If the rectangle has area K 2 ( K > 0 ) , find the perpendicular distance from C to MN .

TestHub · Accepted Answer

Place A at the origin and the centre at ( h , h ) , so MN is x + y = h . With C = ( α , β ) , α β = K 2 and ( α − h ) 2 + ( β − h ) 2 = h 2 . Thus ( α + β − h ) 2 = 2 α β = 2 K 2 , and the distance to MN is K .

Mathematics - Circle Question with Solution | TestHub

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