10th Class Mathematics Circles Question Bank Circle

  • question_answer
    Take vertices of a \[\Delta \,ABC\]as centres and draw three circles with centres A, B, C respectively, each touching the other two externally. If the sides of the triangle are AB = a; BC = b, CA = c, find the radii of three circles in terms of a, b, c.

    A)  \[a+b+c,\frac{a-b-c}{2},\frac{a+b-c}{2}\]

    B)  \[\frac{a+b}{2},\frac{b+c}{2},\frac{c+a}{2}\]

    C)  \[\frac{a}{2},\frac{b}{2},\frac{c}{2}\]

    D)  \[\frac{a-b+c}{2},\frac{a+b-c}{2},\frac{b+c-a}{2}\]

    Correct Answer: D

    Solution :

    (d): Mind of a Mathematician Use \[m+n=a;n+p=b,p+m=c\] At this stage itself, the student will know that he has the answer since he has got 3 equations in 3 variables (m, n, p) which can always be solved.


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