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

1. ## 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.

2. Hello, snigdha!

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

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

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

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

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

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

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# inscribe an isosceles triangle in a circle

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