Math Is Fun Forum

SPARKS_CHAN

Member

Registered: 2014-12-05

Posts: 15

DIFFICULT (for me) GEO PROBLEMS

In the figure, if MR=MK, the measure of arc MK is 130 degrees, and measure of arc MQ is 28 degrees, then what is angle RPK, in degrees?

Points A and B are on circle O such that arc AB is 80 degrees. A circle is constructed that passes through A, B, and O. Find the measure of arc AOB on this circle.

In the figure below, EF is a diameter of the circle. What is the measure of angle ABC, in degrees?

Last edited by SPARKS_CHAN (2015-01-20 15:54:14)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: DIFFICULT (for me) GEO PROBLEMS

hi SPARKS_CHAN

These can all be done using this property of circles http://www.mathisfunforum.com/viewtopic.php?id=17799 post 6

You will also need isosceles triangles and angles along a straight line = 180.

Q1. Mark the centre of the circle as point C.  Join K, M, Q, and R to C with radius lines.

Then, for example, MCK = 130, and MRK = 65.

Keep working around the diagram using all the above rules to work out every angle.

Q2.  Similarly, call the centre of the small circle point C.  Join AC and BC.  Once again use the angle properties of a circle.

Q3. Same again.  I used the property to work out AOE and COF, and gradually progressed round the diagram working out every angle.

Hope that's enough of a hint.  Post back if you need more.   

Bob

Last edited by Bob (2015-01-21 01:02:23)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

SPARKS_CHAN

Member

Registered: 2014-12-05

Posts: 15

Re: DIFFICULT (for me) GEO PROBLEMS

hi SPARKS_CHAN

These can all be done using this property of circles http://www.mathisfunforum.com/viewtopic.php?id=17799 post 6

You will also need isosceles triangles and angles along a straight line = 180.

Q1. Mark the centre of the circle as point C.  Join K, M, Q, and R to C with radius lines.

Then, for example, MCK = 130, and MRK = 65.

Keep working around the diagram using all the above rules to work out every angle.

Q2.  Similarly, call the centre of the small circle point C.  Join AC and BC.  Once again use the angle properties of a circle.

Q3. Same again.  I used the property to work out AOE and COF, and gradually progressed round the diagram working out every angle.

Hope that's enough of a hint.  Post back if you need more.   

Bob

For (1) I'm still confused how you get RPK.

EDIT: Nevermind, I got it!

Last edited by SPARKS_CHAN (2015-01-21 06:09:55)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: DIFFICULT (for me) GEO PROBLEMS

Well done!  That's my answer to. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

adpqadpq

Member

Registered: 2017-02-03

Posts: 18

Re: DIFFICULT (for me) GEO PROBLEMS

Could you help me with q3?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: DIFFICULT (for me) GEO PROBLEMS

Hi;

I do not see the problem can you post it?

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