In the figure,angle acb=90 and radius of big circle=2cm,then the radius of small circle is(in cm)

Dear student

In the diagram

we join the line joining the centres and draw perpendiculars from centre to AC and BC

in triangle POQ

PO2=PQ2+OQ2(2+x)2=(2-x)2+(2-x)2x2+4x+4=2x2-4x+8x2-8x+4=0x=8±64-162=8±482=4±23x=4-23 as x is less than 2
​Regards

 

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