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Find the radius of the circle inscribed in the24 and15triangle formed by the line 3x + 4y=24the co-ordinate axes. |
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Answer» AB & AC are coordinate axes. BC line represents 3x + 4y =24For x=0, y= 6& for y=0, x= 8Hence, the vertices of right triangle are A(0,0), B(8,0) & C(0,6)So, AB =8, AC = 6 & BC = 10 ( by Pythagoras law)And ADOF will be square with side r.Inscribed circle is with centre O & radius rSince inscribed circle centre lies on the angle bisectors of the triangle.So, triangle ODB is congruent to triangle OEB (by RHS congruence criterion, or by AAS congruence corollary)So, BD = BE = (8-r)Similarly CF = CE = (6-r)Therefore, BE + CE = (8-r) +(6-r)=> BC = 14 -2r=> 10 = 14–2r=> 2r = 4=> r= 2 |
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