Find the 13

Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].

Result

e = (Correct answer is: ) OK

Solution:

A[1,−2];B[8,−3];C[9,4]. S=AC/2 x0=(9−1)/2=4 y0=(4−(−2))/2=3  AB: a=1   a⋅ 1+b⋅ (−2)+c=0 a⋅ 8+b⋅ (−3)+c=0 1⋅ 1+b⋅ (−2)+c=0 1⋅ 8+b⋅ (−3)+c=0  2b−c=1 3b−c=8  b=7 c=13   v=a2+b2=12+72=5 2≐7.0711  r=a⋅ x0+b⋅ y0+cv=1⋅ 4+7⋅ 3+137.0711≐5.374  R=r2=5.3742=72225=28.88  e:(x−x0)2+(y−y0)2=r2 e:(x−4)2+(y−3)2=28.88

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