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Math Help - isosceles triangle inscribed in a circle, find the circle's radius....

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    isosceles triangle inscribed in a circle, find the circle's radius....

    PQR is an isosceles ,inscribed in a circle with centre O, such that PQ=PR=13cm and QR=10cm. Find the radius of the circle.
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    Hello, snigdha!

    Isosceles \Delta PQR is inscribed in a circle with center O
    such that: . PQ=PR=13\text{ cm and }QR=10\text{ cm.}
    Find the radius of the circle.
    Code:
                    P
                  * o *
              *    /|\    * 
            *     / | \     *
           *     /  |r \     * 
                /   |   \ 13 
          *    /    |    \    * 
          *   /    O*   r \   *
          *  /      |  *   \  * 
            /       |     * \
         Q o- - - - o - - - -o R 
            *       S   5   * 
              *           *
                  * * *

    In right triangle PSR\!:\;PS^2 + 5^2 \:=\:13^2 \quad\Rightarrow\quad PS = 12

    . . Then: . OS \,=\,12-r


    In right triangle OSR\!:\;\;OS^2 + SR^2 \,=\,OR^2 \quad\Rightarrow\quad (12-r)^2 + 5^2 \:=\:r^2

    And we have: . 144 - 24t + r^2 + 25 \:=\:r^2 \quad\Rightarrow\quad -24r \:=\:-169

    . . Therefore: . r \;=\;\frac{169}{24}\text{ cm}

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