O is any point inside a rectangle abcd

Asked by admin @ 31/08/2021 in Math viewed by 311 People

O is any point inside a rectangle ABCD. prove that OB^2 + OD^2 = OA^2 + OC^2

Answered by admin @ 31/08/2021

We draw PQ ║AB ║CD as shown in figure,
ABCD is a rectangle , it means ABPQ and PQDC are also rectangle
For , ABPQ ,
AP = BQ [opposite sides are equal ]

For, PQDC
PD = QC [ opposite sides are equal ]

now, for ∆OPD,
OD² = OP² + PD² ------(1)

For, ∆OQB,
OB² = OQ² + BQ² --------(2)

add equations (1) and (2),
OB² + OD² = (OP² + PD²)+ (OQ² + BQ²)
= (OP² + CQ²) + (OQ² + AP²)

as you can see figure,
∆OPA and ∆OQC are also right angled triangles
For, ∆OCQ ⇒OQ² + CQ² = OC²
For,∆OPA ⇒OP² + AP² = OA² , put it above

Now ,
OB² + OD² = OC² + OA²
Hence, proved //

Which statement best explains how the alliteration in this excerpt from alfred noyes's poem "the highwayman" contributes to its meaning? o a. the repetition of the "b" sound in lines 4 and 5 points to the importance of the color black o b. the repetition of the "s" sound in line 1 imitates the silence of the highwayman's movements, o c. the repetition of the "w" sound in line 3 reinforces the sound of whistling o d. the repetition of the "t" sound in line 6 emphasizes the idea of love.

Asked by maham237 @ 11/01/2021 in English viewed by 391 persons

O is any point inside a rectangle abcd

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