Junior Exam J2
Each question is worth 7 marks.
Time: 4 hours
No books, notes or calculators allowed.
Note: You must prove your answer.
Let be the diameter of circle . Let be a point on line outside . A tangent from touches at point . The bisector of intersects segments and at points and , respectively.
Prove that = .
Let be a trapezium whose parallel sides are and . Let be the intersection of the trapezium's diagonals and . Suppose further that , and that is the bisector of .
What is the value of ?
Point is situated on the hypotenuse of right-angled triangle , and satisfies
Points and lie on sides and , respectively, of triangle . It is known that and .
Prove that .
Let be the circumcentre of acute triangle . A circle passing through points , and intersects line for a second time at point and intersects line for a second time at point .
Prove that lines and are perpendicular.