# triangleWatch

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#1
Q. In triangle ABC, Let O be the point where the perpendicular bisectors of AB, BC and CA intersect. (You may find it useful to consider an isosceles triangle)

Prove that angle BOA =2* angle BCA.

I drew a diagram but im still not too sure on how to approach proving this. If O were the centre of the circumscribed circle of the triangle then the result is obvious through circle theorems (angle at centre is twice angle at circumference) so should i go about showing that O is the centre of the circumscribed circle?
0
5 years ago
#2
(Original post by IceKidd)
Q. In triangle ABC, Let O be the point where the perpendicular bisectors of AB, BC and CA intersect. (You may find it useful to consider an isosceles triangle)

Prove that angle BOA =2* angle BCA.

I drew a diagram but im still not too sure on how to approach proving this. If O were the centre of the circumscribed circle of the triangle then the result is obvious through circle theorems (angle at centre is twice angle at circumference) so should i go about showing that O is the centre of the circumscribed circle?
The sides of the triangle are chords of the circumscribed circle. Where is the centre?
0
#3
(Original post by brianeverit)
The sides of the triangle are chords of the circumscribed circle. Where is the centre?
I dont knos. My circle geometrys not very good btw.
0
5 years ago
#4
(Original post by IceKidd)
I dont knos. My circle geometrys not very good btw.
Never mind. At least you have fine literacy skills.

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#5
(Original post by Mr M)
Never mind. At least you have fine literacy skills.

ino but what do you know about circles
0
5 years ago
#6
(Original post by IceKidd)
I dont knos. My circle geometrys not very good btw.
The perpendicular bisector of any chord passes through the centre of the circle
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#7
(Original post by brianeverit)
The perpendicular bisector of any chord passes through the centre of the circle
so its sufficient just to say that the point at which two if the perp bisectors intersect must be the centre. from which the result easuy follows?

btw for the DE module note you had. do you have that for any of the other modules on MEI
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5 years ago
#8
(Original post by IceKidd)
so its sufficient just to say that the point at which two if the perp bisectors intersect must be the centre. from which the result easuy follows?

btw for the DE module note you had. do you have that for any of the other modules on MEI
I wish you would preview your posts before submitting them.
I presume you intended writing
so is it sufficient just to say that the point at which two of the perp bisectors intersect must be the centre. from which the result easily follows?
I don't have the same kind of notes for other modules but I do have some sets of revision notes.
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