Question

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

Answer 1

Answer:

To prove:OB

2

+ OD

2

=OA

2

+ OC

2

Prof. Draw a line PQ || BC

⇒ PQ∣∣AD

All angles of rectangular are 90o

∠A=∠B=∠C=∠D=90

∘

Since, PQ || BC and AB is transversal.

∠APO=∠B (corresponding angles)

∠APO=90

∘

Similarly, ∠BPO=90

∘

, ∠DQO=90

∘

, ∠CQD=90

∘

Using Pythagoras theorem,

In ΔOPB,

(OB)

2

=(BP)

2

+(OP)

2

...(1)

In ΔOQD,

(OD)

2

=(OQ)

2

+(DQ)

2

...(2)

Similarly

(OC)

2

=OQ

2

+CQ

2

...(3)

(OA)

2

=(AP)

2

+(OP)

2

...(4)

Adding (1) and (2)

(OB)

2

+(OD)

2

= BP

2

+OP

2

+OQ

2

+DQ

2

=(CQ)

2

+(OP)

2

+(OQ)

2

+(AP)

2

=OC

2

+DA

2

.

BP=CQ

DQ=AP

Step-by-step explanation:

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