Question

In the figure, if B1, B2, B3,...... and A1,A2, A3,..... have been marked at equal distances. In what ratio C divides AB?

Answer 1

Given :- In the figure, if B1, B2, B3,...... and A1,A2, A3,..... have been marked at equal distances. In what ratio C divides AB ? (Refer to image also.)

Solution :-

Let us assume that, the distance between B and B1 is 1 unit .

given that, B1, B2, B3,...... have been marked at equal distances.

Then,

→ BB1 = B1B2= B2B3 = B3B4 = B4B5 = 1 unit .

Therefore,

→ BB5 = 5 units.

Similarly, Let distance between A and A1 also 1 unit.

given that, A1,A2, A3,..... have been marked at equal distances .

Then,

→ AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7 = A7A8 = 1 unit .

Therefore,

→ AA8 = 8 units.

Now, n ACA8 and BCB5 , we have,

→ ∠ACA8 = ∠BCB5 (vertically opposite Angle)

→ ∠A8AC = ∠B5BC (Alternate angles)

So,

→ ACA8 ~ BCB5 (By AA Similarity)

Therefore,

→ AC/BC =AA8/BB5 (By CPCT)

→ AC/BC = 8/5

→ AC : BC = 8:5 . (Ans.)

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3.

In the fig, AB || CD,FIND x.(Hint:Prove that AOB-COD).

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Answer 2

THE RATIO IN WHICH IT DIVIDES IS 8 :5