A circular table is pushed into the corner of a square room

A circular table is pushed into the corner of a square room so that a point P on the edge of the table is 8 cm from one wall and 9 cm from the other wall as shown. Find the radius of the circular table in inches.

Solution

A circular table is pushed into the corner of a square room

edge of the table is 9 cm from one wall

edge of the table is 8 cm from anothert wall

assume that two walls from a coordinate axis

and circular table is a circle

thus above figure represents a circle touches both the axis

also assume that both are in first quadrant

since circle touches both the axis take r be radius of the circle

the equation of the circle is (x-r)²+(y-r)²=r²            (1)

and the distance from one axis is 8 cm and from another axis is 9cm

thus the point (9,8) is on the circle therefore it satisfies the circle equation(1)

(9-r)²+(8-r)²=r²

r²-18r-16r+81+64=0

r²-34r+145=0

r²-29r-5r+145=0

(r-5)(r-29)=0

then r=5       and       r=29

r=5 does not satify the condition that the edge of table 9cm from the wall

thus radius is 29cm.

radius of thecircle is 29cm

since 1 cm is equal to 0.3937 inches

hence 29cm     is equal to              29 * 0.3937=11.4173inches

thus radius is 11.4173 inches.