# 2. Three circles with centres A, B and C touch externally each other. The radius of circle with centre Ais x cm, radius of circle with centre B has radius 6 cm and with centre C has radius 20cm.If angle BAC is 90 frame an equation in x

$Given\;that\;\triangle ABC\;is\;right\;angle\;triangle\;and\;\angle BAC=90^{\circ}\\* consider\;the\;figure\\* In\;\triangle ABC\\* BC^2=AB^2+AC^2\\*AC=20+x\\* AB=6+x\\* BC=20+6=26\;cm\\* 26^2=(x+20)^2+(x+6)^2\\* \Rightarrow 676=400+x^2+40x+36+x^2+12x \\*\Rightarrow 2x^2+52x-240=0\\*\Rightarrow x^2+26x-120=0\\* \therefore x^2+26x-120=0\;is\;the\;required\;equation\;in\;x$

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