Question

9. Point O is in the interior of a
rectangle ABCD.OA, OB. OC & OD
are joined. The length of OA. OB &
OC are shown in the figure below
here the value of 'OD' is
3 cm
3​

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, 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 2 +OS 2 )+(OQ 2 +SD 2 )OA 2+OC 2=(BQ 2+OQ2 )+(OS 2 +SD 2 )OA 2 +OC2 =OB 2 +OD 2 (Considering right triangles OSD and OBQ)