# Make point D with given angles

Nikol Dimitrova shared this question 1 year ago

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; Bonjour,

une solution en utilisant les angles inscrits et angles au centre : 1

Attached a solution with approximation 1

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? 1

Use the very nice soltuion from Patrick an fix the Points B and C with the given Angles. 1

Like that :  1

Bonjour,

une solution en utilisant les angles inscrits et angles au centre : 1

Thank you so much! Can you explain to me what exactly did you do? 1

See the property of the inscribed angles and center angle:

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). 1

Thank you! I will be very grateful if you allow me to ask you sth more about the drawing. :) Can I pm you? 1

"Can I pm you ?"

Sorry, GGB doesn't want that !!!

lol !

... 