2

Part of 2011 NZMOC Camp Selection Problems

Problems(2)

intersection of circles lies in 3rd side (2011 NZOMC Camp Sel. J2)

Source:

Let an acute angled triangle

ABC

be given. Prove that the circles whose diameters are

AB

AC

have a point of intersection on

BC

geometrydiameter

max angle, altitude tangent to circumcircle (2011 NZOMC Camp Sel. S2)

Source:

ABC

, the altitude from

B

is tangent to the circumcircle of

ABC

. Prove that the largest angle of the triangle is between

90^o

135^o

. If the altitudes from both

B

C

are tangent to the circumcircle, then what are the angles of the triangle?

geometrycircumcirclealtitudeangleangles