HARD
IOQM - PRMO and RMO
IMPORTANT
Earn 100

Let ABC be a triangle such that AB=AC. Suppose the tangent to the circumcircle of ABC at B is perpendicular to AC. Find ABC measured in degrees.

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Important Questions on Triangle

HARD
IOQM - PRMO and RMO
IMPORTANT
The centre of the circle passing through the midpoints of the sides of an isosceles triangle ABC lies on the circumcircle of triangle ABC. If the larger angle of triangle ABC is α° and the smaller one is β°, then what is the value of α-β?
MEDIUM
IOQM - PRMO and RMO
IMPORTANT
A friction-less board has the shape of an equilateral triangle of side length 1 meter with bouncing walls along the sides. A tiny super bouncy ball is fired from vertex A towards the side BC. The ball bounces off the walls of the board nine times before it hits a vertex for the first time. The bounces are such that the angle of incidence equals the angle of reflection. The distance travelled by the ball in meters is of the form N, where N is an integer. What is the value of N?
HARD
IOQM - PRMO and RMO
IMPORTANT
Let ABC be an acute angled triangle with AB=15 and BC=8. Let D be a point on AB such that BD=BC. Consider points E on AC such that DEB=BEC. If α denotes the product of all possible values of AE, find [α]10, whereα is the integer part of α.
HARD
IOQM - PRMO and RMO
IMPORTANT
Let AB be a chord of a circle with centre O. Let C be a point on the circle such that ABC=30° and O lies inside the triangle ABC. Let D be a point on AB such that DCO=OCB=20°. Find the measure of CDO in degrees.
HARD
IOQM - PRMO and RMO
IMPORTANT
Triangles ABC and DEF are such that A=D, AB=DE=17, BC=EF=10 and AC-DF=12. What is AC+DF?
HARD
IOQM - PRMO and RMO
IMPORTANT
Let ABC be an acute-angled triangle and let H be its orthocentre. Let G1, G2 and G3 be the centroids of the triangles HBC, HCA and HAB, respectively. If the area of triangle G1G2G3 is 7 units, what is the area of triangle ABC?
HARD
IOQM - PRMO and RMO
IMPORTANT
Let D be an interior point of the side BC of a triangle ABC. Let I1 and I2 be the incentres of triangles ABD and ACD, respectively. Let AI1 and AI2 meet BC in E and F, respectively. If BI1E=60°, what is the measure of Cl2F in degrees?