Question

o is any point inside a rectangle ABCD . prove that OB²+OD²=OA²+OC²​

Answer 1

Answer:

(OA)^2+(OC)^2=(OB)^2+(OD)^2

Step-by-step explanation:

Now, (OA)^2 +(OC)^2 =(AS)^2 +(OS)^2 +(OQ)^2+(QC )^2

(Considering right triangles ASO and COQ)

But AS=BQ and QC=SD, Therefore,

(OA)^2+(OC)^2 =(BQ)^ + (OS )^2+(OQ)^2 +(SD) ^2

(OA)^2 +(OC)^2 =(BQ)^2 +(OQ)^2)+(OS)^2+(SD) ^2

(OA)^2+(OC)^2 =(OB)^2 +(OD)^2

(Considering right triangles OSD and OBQ)