Make point D with given angles

Nikol Dimitrova shared this question 1 year ago
Answered

Hello,

I am interested in GeoGebra and I am wondering if there is a fast way to make point D:

  • OD > r (O is the centre of the circle)
  • B and D are in different half-plains
  • angle BDC = 20 degrees; angle BDA = 35 degrees;

Thank you in advance!

Best Answer
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Bonjour,

une solution en utilisant les angles inscrits et angles au centre :

Comments (9)

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Attached a solution with approximation

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I appreciate your help! But I forgot to write that triangle ABC is isosceles: angle BAC = 40 degrees and angle BCA = 70 degrees. I am not very good with GeoGebra, and I didn't understand how did you get the point D?

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Use the very nice soltuion from Patrick an fix the Points B and C with the given Angles.

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Like that :

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Bonjour,

une solution en utilisant les angles inscrits et angles au centre :

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Thank you so much! Can you explain to me what exactly did you do?

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See the property of the inscribed angles and center angle:

https://www.geogebra.org/m/...


angle BDA = 35 ° so D is on the circle (e) passing through B and A of center E.

E is a point of the mediator of [AB] such that angleAEB = 2 * 35 = 70 °.

The triangle AEB being isosceles, angleBAE = angleEBA, therefore angle BAE = (180-70) / 2 = 55 °

E is then the intersection of the line (i) making an angle of 55 ° with [AB] , and the perpendicular bisector (h).


angle CDB = 20 ° so D is on the circle (p) passing through B and C of center G.

G is a point in the mediator of [BC] such that angleAEB = 2 * 20 = 40 °.

The triangle BCG is isosceles, angleCBG = angleGCB, so angle CBG = (180-40) / 2 = 70 °

G is then the intersection of the line (k) making an angle of 55 ° with [BC] , and the perpendicular bisector (j).


D is the intersection of the two circles (e) and (p).

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Thank you! I will be very grateful if you allow me to ask you sth more about the drawing. :) Can I pm you?

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"Can I pm you ?"

Sorry, GGB doesn't want that !!!

lol !

...

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