9

Part of 2019 India PRMO

Problems(2)

Simple Fractions

Source:

Let the rational number

p/q

be closest to but not equal to

22/7

among all rational numbers with denominator

< 100

. What is the value of

p - 3q

Circumcentre on circumcircle

Source: PRMO 2019 Leg 2 P9

The centre of the circle passing through the midpoints of the sides of am isosceles triangle

ABC

lies on the circumcircle of triangle

ABC

. If the larger angle of triangle

ABC

\alpha^{\circ}

and the smaller one

\beta^{\circ}

then what is the value of

\alpha-\beta

geometryPRMOcircumcircle