Using a ruler and a pair of compasses only construct triangle ABC such that AB=8cm,angle ABC=60degree and angle BAC =75degree,Locate the point O inside triangle ABC equidistant from A,B and C. Construct the circle with center O, which passes through A.Measure OA and angle ACD

Question

Using a ruler and a pair of compasses only construct triangle ABC such that AB=8cm,angle ABC=60degree and angle BAC =75degree,Locate the point O inside triangle ABC equidistant from A,B and C. Construct the circle with center O, which passes through A.Measure OA and  angle ACD

oobleck · Answer

no idea where D is
Clearly, ∡C = 45°
If O is equidistant from A,B,C, then it is the circumcenter of ABC. That is, it lies on the perpendicular bisectors of each side.
So, to construct ABC,
draw side AB
construct angles A and B (you can do this by constructing a 60° angle at A, and a 60° + 15° angle at B.)
C lies on the intersection of the rays from A and B.
Construct two of the perpendicular bisectors. O is at their intersection
google can help with examples of each of these steps

Triangle · Answer

ABC BASE AB=8CM 90DEGREE B 60DEGREE