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°.

Easy Math Editor

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Comments

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

Reynan Henry - 6 years, 1 month ago

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

Dhaman Trivedi - 6 years, 1 month 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

Reynan Henry - 6 years, 1 month ago

@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 - 6 years, 1 month ago

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

Reynan Henry - 6 years, 1 month ago

@Reynan Henry – Its not a clear link i cant open it

Dhaman Trivedi - 6 years, 1 month ago

@Dhaman Trivedi – Maybe this should help. https://youtu.be/nwOSsjLDACQ

Reynan Henry - 6 years, 1 month ago

@Reynan Henry – Ok thanks. Should i delete this note now? or see more answers?

Dhaman Trivedi - 6 years, 1 month ago

@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 - 6 years, 1 month ago

@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 - 6 years, 1 month ago

Good Question Brother, let me try this one!

Swapnil Das - 6 years, 1 month ago

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

Dhaman Trivedi - 6 years, 1 month ago

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

Swapnil Das - 6 years, 1 month ago

@Swapnil Das – This also that y ∠CAB=∠BCD...and∠DAB=∠CDB this too

Dhaman Trivedi - 6 years, 1 month ago

@Swapnil Das – Waiting for your reply Swapnil.. Just tell me Why the answer is 180°

Dhaman Trivedi - 6 years, 1 month ago

@Swapnil Das – Waiting for your reply Swapnil.. Just tell me Why the answer is 180°.?

Dhaman Trivedi - 6 years, 1 month ago

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

Nihar Mahajan - 6 years, 1 month 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

Dhaman Trivedi - 6 years, 1 month ago

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

Reynan Henry - 6 years, 1 month ago

Do u know that cbda is a kite?

A S - 6 years, 1 month ago

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

Calvin Lin Staff - 6 years, 1 month ago

I have the same question as Calvin Sir

Dhaman Trivedi - 6 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$