Question

Pis any point inside a rectangle ABCD then which of the following is the value of PB2 + PD2​

Answer 1

Answer:

Given, ABCD is a rectangle. O is any point inside the rectangle.

Construction: Construct perpendiculars OP, OQ, OR, OS on each side. 

Now, OA2+OC2=(AS2+OS2)+(OQ2+QC2) (Considering right triangles ASO and COQ)

But AS=BQ and QC=SD, Therefore,

OA2+OC2=(BQ2+OS2)+(OQ2+SD2)

OA2+OC2=(BQ2+OQ2)+(OS2+SD2)

OA2+OC2=OB2+OD2 (Considering right triangles OSD and OBQ)

Answer 2

Answer:

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