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°.

@Calvin Lin
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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

@Reynan Henry
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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?

@Dhaman Trivedi
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Take a look
https://lh4.googleusercontent.com/proxy/EtyNHxDLxZTJK07Ycu6ZHDiCeLxmFMwHE3kovJnNo1217WVMbaghfOKmQUaiwbYYc7kOwWPK6Wp-Y72DhT9AMMmlrtTPiNfKfme-U0AsmB6_BPXiGICzPabmPVrA=w266-h189-nc

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## Comments

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

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

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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

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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.

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https://lh4.googleusercontent.com/proxy/EtyNHxDLxZTJK07Ycu6ZHDiCeLxmFMwHE3kovJnN

o1217WVMbaghfOKmQUaiwbYYc7kOwWPK6Wp-Y72DhT9AMMmlrtTPiNfKfme-U0AsmB6_BPXiGICzPabmPVrA=w266-h189-ncLog in to reply

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Do u know that cbda is a kite?

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I have the same question as Calvin Sir

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

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

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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

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

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Good Question Brother, let me try this one!

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

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

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