Math Is Fun Forum

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Circles #2

ΔDEF has DE=DF and O is a point on DE produced such that a circle with center O can be drawn to touch DF at F. If FE is produced cuts the circle at H, prove that OH is perpendicular to DE

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

atran

Member

Registered: 2013-07-12

Posts: 91

Re: Circles #2

I'm not sure about the description and can't draw what you describe. Can you post the drawing?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Circles #2

hi

Try this.  Colour coded clue.

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

atran

Member

Registered: 2013-07-12

Posts: 91

Re: Circles #2

Thanks Bob.

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: Circles #2

thanks bob for the drawing.
here comes the proof:-

FD is the tangent to OF.
=>  <OFD =90°

In ΔHOF,
<OHE= <OFE

In ΔDEF,
<DEF=<DFE

also, <DFE= 90° - <OFE
               = 90° - <OHE

Now,
       <HEO=<DEF
=>   <HEO=90° - <OHE
=>   <HEO +<OHE= 90°

Now, <HEO + <OHE + <HOE=180°
       => 90°+<HOE =180°
       => <HOE=90°

Hence, HO is perpendicular to OE.
                                              proved.:)

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friendship is tan 90°.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Circles #2

Wow! Thanks Nihar

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: Circles #2

you're most welcome

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friendship is tan 90°.