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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

Agnishom
2013-04-13 02:50:57

Okay Got it Thanks!

bob bundy
2013-04-12 22:54:39

Let O be the point at the centre of the circle.

angle DOC = 2 x angle DAC (angle properties of a circle)

similarly angle COE = 2 x angle CBE

OD = OC = OE = radius

So triangles DOC and COE are congruent => straight line DC = straight line CE => arc DC = arc CE

Bob

Agnishom
2013-04-12 22:37:38

They have one common angle and one right angle so the other angle must be the same.

thanks but I need a way to say that if angle angle DAC = angle CBE, then CD = CE

bob bundy
2013-04-12 17:57:20

Hi Agnishom

For arc CD = arc CE you want angle DAC = angle CBE

See diagram.  Where the altitudes meet the sides I've named those points F and G

So what can you say about triangles AFC and BGC  ?

Bob

Agnishom
2013-04-12 14:12:30

In ΔABC, the perpendicular from vertices A and B on their opposite sides meet (when produced) the circumcircle of the triangle at points D and E respectively.
Prove that arc CD = arc CE

Somebody, please help me with this proof.
Note: You are not allowed to use trigonometry

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