# A Geometrical Circular Problem!!

Hey Brilliants! I found this question in my book. Q-CD is a direct common tangent to two circles intersecting each other at A and B. Then angle CAD + angle CBD is equal to what? The answer is 180°, Now what I wanna know is how the answer came 180°.

Note by Dhaman Trivedi
5 years ago

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Do u know that cbda is a kite?

- 5 years ago

I have the same question as Calvin Sir

- 5 years ago

Can you explain why it is a kite? Are you assuming that the circles are congruent?

Staff - 5 years ago

I happened to see this note and one question came to my mind after observing the figure: Are the two circles congruent?

- 5 years ago

That's the problem what I wrote in question, That's all. I also thought the same but no....No where proved that those are congurent

- 5 years ago

Even if the circles arent congruent. The sum is still 180

- 5 years ago

Its easy right asume ab intersect cd at x then bax equal to bcx

- 5 years ago

I don't got it can you explain in brief?

- 5 years ago

Sorry i cant use the latex hehe. But angle bca is equal to angle bcx (alternate segment theorem) so bca + bcx = 90 analog bad + bdx = 90. Add them all

- 5 years ago

Are you sure about your angles? I think you mean that BAC = BCD instead of BCA = BCX (which is BCD).

Also, I doubt that BCA + BCX = 90, because that is equal to ACX, which is ACD, which is not 90.

You are on the right track, but you just need to ensure that what you write is what you are thinking.

Staff - 5 years ago

Sir Calvin actually I do have the solution of this question, but there are some things where I just ask "Why it is happening" If you say I post my solution of book here and then you explain my Whys. Thanks

- 5 years ago

Oh! OK! Thanks Reynan! You cleared my big doubt. Sorry last question. I dont know much about theories so please tell about what is alternate segment theorem?

- 5 years ago

Take a look

- 5 years ago

Its not a clear link i cant open it

- 5 years ago

Maybe this should help. https://youtu.be/nwOSsjLDACQ

- 5 years ago

Ok thanks. Should i delete this note now? or see more answers?

- 5 years ago

Good Question Brother, let me try this one!

- 5 years ago

Swapnil Das I have given the solution given in book. Just tell me they Whys answer

- 5 years ago

Ya, I just have to prove that the answer is 180.

- 5 years ago

- 5 years ago

- 5 years ago

This also that y ∠CAB=∠BCD...and∠DAB=∠CDB this too

- 5 years ago