Any mathematicians out there?
11 May 2001, 11:07 PM
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FamilyXRS - The answer to 4 is....
Take triangle CDA, Angle CDA = 90, ACB = 70 therfore CAD = 20
As howard said "Angles in the same segment are equal." i.e. if you take chord CP then CAP = CBP. (The diameter case above is just a special case of this where the chord is a diameter and the angle is 90)
Now we know CAP is 20 (from CAD above) therefore CBP = 20 (CP is the common chord)
We also know CBE = 20 (from triangle CEB, angle CEB = 90, ECB =70)
therefore look at triangle HBP. the line BD bisects angle HBP and is perpendicular to HP therefore IT bisects line HP i.e. D is the midpoint
suggest http://www.easymaths.com/round_trips.htm for a better description of the theories.
Question 5) Why does scoobynet drive me to search google at 11.00 pm for circle theories
Dean
[Edited by dsmith - 11/5/2001 11:14:31 PM]
Take triangle CDA, Angle CDA = 90, ACB = 70 therfore CAD = 20
As howard said "Angles in the same segment are equal." i.e. if you take chord CP then CAP = CBP. (The diameter case above is just a special case of this where the chord is a diameter and the angle is 90)
Now we know CAP is 20 (from CAD above) therefore CBP = 20 (CP is the common chord)
We also know CBE = 20 (from triangle CEB, angle CEB = 90, ECB =70)
therefore look at triangle HBP. the line BD bisects angle HBP and is perpendicular to HP therefore IT bisects line HP i.e. D is the midpoint
suggest http://www.easymaths.com/round_trips.htm for a better description of the theories.
Question 5) Why does scoobynet drive me to search google at 11.00 pm for circle theories
Dean
[Edited by dsmith - 11/5/2001 11:14:31 PM]
11 July 2001, 08:51 PM
#2
Scooby Senior
Dean,
I have a message from she who must be obeyed. I do of course disassociate myself from all her remarks (standard practice):
"Dean Worship.
Many thanks Deano. You'll be my first port of call for maths in future.
MrsXRS
ps are you good at anything else?"
[Edited by XRS - 11/7/2001 10:09:40 PM]
I have a message from she who must be obeyed. I do of course disassociate myself from all her remarks (standard practice):
"Dean Worship.
Many thanks Deano. You'll be my first port of call for maths in future.
MrsXRS
ps are you good at anything else?"
[Edited by XRS - 11/7/2001 10:09:40 PM]
05 November 2001, 03:49 PM
#3
Scooby Senior
My son has this maths problem. It's got to him so much that he's had to spend the day playing golf to forget about it. We can do 1 and 2, but the years have taken their toll as far as the rest is concerned. Anyone have any ideas?
ABC is a triangle whose corners lie on the circumference of a circle. D lies on BC such that AD is perpendicular to BC, and E lies on AC such that BE is perpendicular to AC. Angle ACB=70. AD and BE intersect at H.
1. Draw a sketch to illustrate the above information.
2. Calculate angles EBC and DAC
3. Explain why it is possible to draw a circle through ABD and E and state where the centre of this circle lies
4. AD is continued to point P on the circle. State with reason the size of the angle CBP and explain why D is the midpoint of HP.
Have fun thinking about it anyway!
ABC is a triangle whose corners lie on the circumference of a circle. D lies on BC such that AD is perpendicular to BC, and E lies on AC such that BE is perpendicular to AC. Angle ACB=70. AD and BE intersect at H.
1. Draw a sketch to illustrate the above information.
2. Calculate angles EBC and DAC
3. Explain why it is possible to draw a circle through ABD and E and state where the centre of this circle lies
4. AD is continued to point P on the circle. State with reason the size of the angle CBP and explain why D is the midpoint of HP.
Have fun thinking about it anyway!
05 November 2001, 04:23 PM
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My brain hurts..............noooooooooooooooooooooooooooooo .........its school again.............flash backs..........bullying.........conkers........... dinner ladies.........semelina.............ahhhhhhhhhhhhh hhhhhhhhhhh
05 November 2001, 05:00 PM
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I can do 3) ....
if you form a triangle from a diameter and any point on the circumference than angle at the circumference will be 90 degrees.
Because Angle AEB and ADB are both 90 a circle will go through AEDB (AB is a diameter with E and D two points on the circumference). Centre would therfore be at the midpoint of AB.
Still thinking about 4)
if you form a triangle from a diameter and any point on the circumference than angle at the circumference will be 90 degrees.
Because Angle AEB and ADB are both 90 a circle will go through AEDB (AB is a diameter with E and D two points on the circumference). Centre would therfore be at the midpoint of AB.
Still thinking about 4)
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05 November 2001, 10:36 PM
#8
Scooby Senior
Howard,
Line AP passed through H, and therefore must be the diameter of the circle. Thus, ABP is a triangle in a circle which has one side as the diameter, and all points resting on a circle, so therefore . as you pointed out, ABP is 90. The triangle HAB is an isosceles traingle because AH=HB - they are both radii, therefore HAB=ABH=(180-110)/2. As ABP = 90, CBP must = 35 (I think), but I still don't know why D is the mid-point of HP.
Nevertheless, you have been very helpful (even brilliant) - many thanks.
MrsXRS
06 November 2001, 11:01 AM
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Exactly why do kids need to learn this kinda stuff?
If they want to go into engineering etc, let em do it then.
The best thing to teach kids is how to learn, then whatever they are interested in, they can pick it up. With the pace of change moving so quickly, the facts we learned at school are now out of date. Therefore learning to learn new stuff is of primary importance.
I hated maths, saw no need for pure maths what so ever
If they want to go into engineering etc, let em do it then.
The best thing to teach kids is how to learn, then whatever they are interested in, they can pick it up. With the pace of change moving so quickly, the facts we learned at school are now out of date. Therefore learning to learn new stuff is of primary importance.
I hated maths, saw no need for pure maths what so ever
06 November 2001, 02:03 PM
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Family fight........
Neil, you need to learn stuff like this so that years later when someone posts a similar question on a bbs you can post a big diagram and an answer and some people would think you are clever.
Seems obvious really
Neil, you need to learn stuff like this so that years later when someone posts a similar question on a bbs you can post a big diagram and an answer and some people would think you are clever.
Seems obvious really
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