



 
Hi Anita, Since you can rotate the circle inside the larger triangle without changing any of the dimensions I chose to have the vertices of the smaller triangle at the points of tangency of the sides of larger triangle to the circle. The measure of angle EFD is 60^{o} and this angle is subtended by the chord ED. But ED subtends the angle EGD at the centre of the circle so the measure of the angle EGD is 120^{o} and the measure of the angle HGD is therefore 60^{o}. Angle GDA is a right angle so the measure of angle DAG is 30^{o}. Triangle AHD is a right triangle and hence it is a 306090 triangle. Thus 2HD = AD and thus
Harley  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 