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geometry

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find the radius of the circle inscribed in a triangle whose sides are 15cm, 17 cm and 8cm?

  • geometry -

    make a diagram
    Triangle ABC with AB=17, BC=8 and AC = 15

    Did you realize that your triangle is right-angled, with angle C = 90° ?

    let the points of contact of the circle be
    D on BC, E on AC, and F on AB

    Two properties we can use ...
    1. The centre of the incscribed circle lies on the angle bisectors of the triangle, and
    2. BF=BC , AE=AF, and DC = EC, by the tangent properties

    let the radius be r,
    since the 90° is bisected, DC = r
    then BD= 8-r, and of course by #2 BF=8-r
    then AF= 9+r and AE = 15-r

    I see two similar triangles at the top, so

    r/(9+r) = r/(15-r)

    solve for r

  • geometry -

    3cm

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