Question

Please solve the sums which are circled...

Answer 1

Answer:

Step-by-step explanation:

Given, a quadrilateral ABCD in which the diagonals AC and BD intersect each other at point O.

i) 

It is given that, AO = 2 CO and BO = 2 DO

=> AO/CO = 2/1 and. BO/DO = 2/1

=> AO/CO = BO/DO = 2/1 - - - - - - - - (1)

Now, in triangle AOB and triangle COD, we have

AO/CO = BO/DO   [from (1)]

Also, ∠AOB = ∠COD  [vertically opposite angles]

⇒ ΔAOB ~ ΔCOD  [SAS similarity]  

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ii)

From (1), we have

AO/CO = BO/DO

On cross multiplication, we get

OA × OD = OB × OC 

[Hence proved] 

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HOPE IT HELPS U !!!