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Let s denotes the semi-perimeter of a De...

Let s denotes the semi-perimeter of a `DeltaABC` in which BC=a, CA=b and AB=c. If a circle touches the sides BC, CA, AB, at D, E, F, respectively. Prove that BD=s-b.

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Let's denote the semi-perimeter of a triangle ABC in which BC = a, CA = 5, AB = c. If a circle touches the side BC, CA, AB at D, E, F respectively, prove that BD = S-b.

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Knowledge Check

  • The in circle of Delta ABC touches the sides BC, CA and AB at D, E and F respectively. Then AF + BD + CE is equal to :

    A
    `(1)/(2)` (Perimeter of `Delta` ABC)
    B
    `(1)/(3)` (Perimeter of `Delta` ABC)
    C
    `(1)/(4)` (Perimeter of `Delta` ABC)
    D
    Perimeter of `Delta` ABC

  • Let angleA=23^(@), angleB=75^(@) and angleC=82^(@) be the angles of DeltaABC . The incircle of DeltaABC touches the sides BC, CA, AB at points D, E, F respectively. Let r', r_(1)^(') respectively be the inradius, exradius opposite to vertex D of DeltaDEF and r be inradius of DeltaABC , then Q. (r')/(r)=

    A
    `"sin"(A)/(2)+"sin"(B)/(2)+"sin"(C )/(2)-1`
    B
    `1-"sin"(A)/(2)+"sin"(B)/(2)+"sin"(C )/(2)`
    C
    `"cos"(A)/(2)+"cos"(B)/(2)+"cos"(C )/(2)-1`
    D
    `1-"cos"(A)/(2)+"cos"(B)/(2)+"cos"(C )/(2)`

  • Let angleA=23^(@), angleB=75^(@) and angleC=82^(@) be the angles of DeltaABC . The incircle of DeltaABC touches the sides BC, CA, AB at points D, E, F respectively. Let r', r_(1)^(') respectively be the inradius, exradius opposite to vertex D of DeltaDEF and r be inradius of DeltaABC , then Q. (r_(1)^('))/(r )=

    A
    `"sin"(A)/(2)+"sin"(B)/(2)+"sin"(C )/(2)-1`
    B
    `1-"sin"(A)/(2)+"sin"(B)/(2)+"sin"(C )/(2)`
    C
    `"cos"(A)/(2)+"cos"(B)/(2)+"cos"(C )/(2)-1`
    D
    `1-"cos"(A)/(2)+"cos"(B)/(2)+"cos"(C )/(2)`

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    The incircle of an isosceles triangle ABC , with AB=AC , touches the sides AB , BC , CA at D,E and F respectively. Prove that E bisects BC .

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    Let angleA=23^(@), angleB=75^(@) and angleC=82^(@) be the angles of DeltaABC . The incircle of DeltaABC touches the sides BC, CA, AB at points D, E, F respectively. Let r', r_(1)^(') respectively be the inradius, exradius opposite to vertex D of DeltaDEF and r be inradius of DeltaABC , then Q. (r')/(r)=

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