Circle Geometry:Finding Unknown Angle

• Jul 4th 2010, 06:57 AM
Lukybear
Circle Geometry:Finding Unknown Angle
In diagram arc BC is three times larger than arc AD and angle BEC = 80. Let angle ABD = x and find x.

Here i cannot include the given information into the question. So using the 80 alone, i cannot get any angles...
• Jul 4th 2010, 07:09 AM
malaygoel
Quote:

Originally Posted by Lukybear
In diagram arc BC is three times larger than arc AD

Here i cannot include the given information into the question. So using the 80 alone, i cannot get any angles...

Let O be the centre of circle.
since arcBC is three times arcAD, hence
angle BOC is three times angle AOD(why?)

Can you proceed from here?
• Jul 4th 2010, 08:49 AM
Plato
We know that $\displaystyle 2m\left( {\angle BEC} \right) = m\left( {arc(DA)} \right) + m\left( {arc(BC)} \right)$.
So what is $\displaystyle m\left( {arc(DA)} \right)?$
We know that $\displaystyle 2m\left( {\angle ABD} \right) = m\left( {arc(DA)} \right)$.
• Jul 4th 2010, 04:54 PM
Lukybear
I have no idea malaygoel how to proceed from there. That was the original information i know. Could you please expand on that? For i think thats the method the question wants the students to develop.

Also plato, really sorry, but i cant understanding your use of symbols. Wha is m?
• Jul 4th 2010, 05:00 PM
Plato
Quote:

Originally Posted by Lukybear
Also plato, really sorry, but i cant understanding your use of symbols. Wha is m?

With all due respect, it you have no idea about what I wrote in my reply then you are simply not at the level of mathematical maturity to have been assigned this question.
• Jul 4th 2010, 08:06 PM
Lukybear
Well mabey. But i do think since i am in a different part of the world, that different symbology apply to same meaning.

But without going into that, i am still very interested in what m means. I understanding arc and angle. Considering what you are saying, you might be right. Then i would assume that a easier, more fundemental approach to this question was suitable.
• Jul 5th 2010, 04:37 AM
sa-ri-ga-ma
circle
Let O be the center of the circle

It is given that

$\displaystyle \angle{BOC} = 3\angle{AOD}$

Now $\displaystyle \angle{BOC} = 2 \angle{BAC}$

and $\displaystyle \angle{AOD} = 2\angle{ABD}$

But $\displaystyle \angle{BAC} + \angle{ABD}= 80 degrees$

Substitute the values and find angle ABD.
• Jul 6th 2010, 03:44 AM
bjhopper
just a comment

The measure (m) 0f an angle between two chords in a circle equals half the sum of its arcs.

bjh
• Jul 7th 2010, 08:16 AM
Wilmer
m[angle ABC] means "measure" of angle ABC: always thought that was silly and misleading.

Like for line AB = x, we don't use m[line AB] = x; so why treat angles differently?

That's my opinion: I respect yours, but if it's not same as mine, then it's wrong :)
• Jul 7th 2010, 07:53 PM
Lukybear
Quote:

Originally Posted by sa-ri-ga-ma
Let O be the center of the circle

It is given that

$\displaystyle \angle{BOC} = 3\angle{AOD}$

Thxs very much. Its so easy once ive seen it.

Now $\displaystyle \angle{BOC} = 2 \angle{BAC}$

and $\displaystyle \angle{AOD} = 2\angle{ABD}$

But $\displaystyle \angle{BAC} + \angle{ABD}= 80 degrees$

Substitute the values and find angle ABD.

Thxs so much. Once ive seen it it becomes so easy.