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
Answers
Answered by
9
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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