Question

Find area of the shaded red region... Point P(-4,-3) Square inscribed in circle, centre (0,0)?

Answer 1

shaded area `=12.5 " units"^2`

Explanation:

let `O(0,0)` be the center of the circle
radius `OA=OB=OC=OD=sqrt(-4^2+(-3)^2)=5`
Area of square `ABCD=|ABCD|=1/2*AC*BD=1/2*10*10=50`
As `F` is the perpendicular reflection of `H` over x-axis,
`=> OH=OF`
Similarly, `OE=OG`
As `ABCD` is a square, `OE=OF=OG=OH`,
and `angleOEA, angleOFB, angleOGC, and angleOHD` are equal.
`=> DeltaOEA, DeltaOFB, DeltaOGC, and DeltaOHD` are congruent.
`=> DeltaOAF, DeltaOBG, DeltaOCH, and DeltaODE` are congruent.
Hence, shaded area `=|OEA|+|OAF|`
`= |ABCD|/4=50/4=12.5 " units"^2`