Question

ABCD is a trapezium such that ABllCD and AB = 3cm.If the diagonals AC and BD intersect at O such that OA / OC = OB / OD = 1 / 2, then calculate DC
please help me
NO SPAMS❌❌❌❌
if spammed I'll REPORT you ​

Answer 1

Step-by-step explanation:

I'll Send you Pic of the Solution...

Answer 2

Answer:

The answer will be 6 cm.

Step-by-step explanation:

According to question, we know :

             AB = 3cm;

             $\frac{AO}{CO} = \frac{OB}{OD} = \frac{1}{2}$;

In the trapezium, there will two triangle form and i.e, ΔAOB and Δ COD.

So, in Δ AOB and Δ COD;

         ∠AOB = ∠COD;  (Since, AC and BD are straight lines joining at O, creating vertically opposite angle.)

          $\frac{AO}{CO} = \frac{OB}{OD}$;     (given)

Hence, ΔAOB  ~  Δ COD (by SAS criterion of similarity).

Since, ΔAOB and Δ COD are similar, we can write;

              $\frac{AO}{CO} = \frac{OB}{OD} = \frac{AC}{DC}$;

               $\frac{AO}{CO} = \frac{OB}{OD} = \frac{AC}{DC} = \frac{1}{2}$;                                       (i)

Here, we'll use a ratio from equation (i) and i.e, ;

              $\frac{AB}{DC} = \frac{1}{2}$;

  Now, we have already given the value of AB, hence;

             $\frac{3}{DC} = \frac{1}{2}$;

After transposing DC to LHS and 2 to RHS, we get;

             3*2 = 1 * DC;

             DC = 6 cm.

That's all.