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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
1 year, 8 months ago

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Its easy right asume ab intersect cd at x then bax equal to bcx Reynan Henry · 1 year, 8 months ago

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@Reynan Henry I don't got it can you explain in brief? Dhaman Trivedi · 1 year, 8 months ago

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@Dhaman Trivedi 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 Reynan Henry · 1 year, 8 months ago

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@Reynan Henry 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. Calvin Lin Staff · 1 year, 8 months ago

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@Calvin Lin 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 Dhaman Trivedi · 1 year, 8 months ago

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@Reynan Henry 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 · 1 year, 8 months ago

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@Dhaman Trivedi Take a look
https://lh4.googleusercontent.com/proxy/EtyNHxDLxZTJK07Ycu6ZHDiCeLxmFMwHE3kovJnNo1217WVMbaghfOKmQUaiwbYYc7kOwWPK6Wp-Y72DhT9AMMmlrtTPiNfKfme-U0AsmB6_BPXiGICzPabmPVrA=w266-h189-nc Reynan Henry · 1 year, 8 months ago

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@Reynan Henry Its not a clear link i cant open it Dhaman Trivedi · 1 year, 8 months ago

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@Dhaman Trivedi Maybe this should help. https://youtu.be/nwOSsjLDACQ Reynan Henry · 1 year, 8 months ago

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@Reynan Henry Ok thanks. Should i delete this note now? or see more answers? Dhaman Trivedi · 1 year, 8 months ago

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Do u know that cbda is a kite? A S · 1 year, 8 months ago

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@A S I have the same question as Calvin Sir Dhaman Trivedi · 1 year, 8 months ago

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@A S Can you explain why it is a kite? Are you assuming that the circles are congruent? Calvin Lin Staff · 1 year, 8 months ago

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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? Nihar Mahajan · 1 year, 8 months ago

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@Nihar Mahajan 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 Dhaman Trivedi · 1 year, 8 months ago

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@Dhaman Trivedi Even if the circles arent congruent. The sum is still 180 Reynan Henry · 1 year, 8 months ago

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Good Question Brother, let me try this one! Swapnil Das · 1 year, 8 months ago

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@Swapnil Das Swapnil Das I have given the solution given in book. Just tell me they Whys answer Dhaman Trivedi · 1 year, 8 months ago

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@Dhaman Trivedi Ya, I just have to prove that the answer is 180. Swapnil Das · 1 year, 8 months ago

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@Swapnil Das This also that y ∠CAB=∠BCD...and∠DAB=∠CDB this too Dhaman Trivedi · 1 year, 8 months ago

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@Swapnil Das Waiting for your reply Swapnil.. Just tell me Why the answer is 180°.? Dhaman Trivedi · 1 year, 8 months ago

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@Swapnil Das Waiting for your reply Swapnil.. Just tell me Why the answer is 180° Dhaman Trivedi · 1 year, 8 months ago

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