In the figure, ABCD is a square inside a circle with centre O The Centre of the square coincides - Maths - Areas Related to Circles

Question

In the figure, ABCD is a square inside a circle with centre O The
Centre of the square coincides with O & the diagonal AC is
horizontal of AP, DQ are vertical & AP = 45 cm, DQ = 25 cm Find
a) the radius of the circle b) side of square c) area of shaded
region

Vijay Kumar Gupta · Accepted Answer

Dear student,

Please find below the solution to the asked query:

The figure is shown below:

aSuppose that AO=x cm, then OD=x cm
The radius of the circle is,  r=OP   =OQ   =OD+DQ   =x+25 cmNote that △PAO is right triangle right angled at ASo by pythagoras theorem, we get            OP2=AP2+AO2⇒x+252=452+x2⇒x2+50x+625=2025+x2⇒50x+625=2025⇒50x=1400⇒x=28Therefore the radius of circle is,    r=x+25     =28+25    =53 cmbFrom right angled triangle AOD, by pythagoras theorem, we get    AD2=AO2+OD2           =x2+x2           =2x2⇒AD=2x2⇒AD=2 x⇒AD=282So the side of square is AD=282 cmcRequired area=Area of the circle-area of the square                           =πr2-side2                           =3
14 ×532-2822                           =8820
26-1568                           =7252
26 cm2

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In the figure, ABCD is a square inside a circle with centre O. The Centre of the square coincides with O & the diagonal AC is horizontal of AP, DQ are vertical & AP = 45 cm, DQ = 25 cm. Find a) the radius of the circle b) side of square c) area of shaded region