O and C are respectively the orthocentre and the circumcentre of an acute angled triangle POR. The points P and O are joined and produced to meet the side QR at S. If ∠POS=60⁰ and ∠QCR = 130°, then ∠RPS = ?

The sides of a triangle are 56 cm, 90 cm and 106 cm. The circumference of its circumcircle is:

The length of two chords AB and AC of a circle are 8 cm and 6 cm and ∠BAC=90º, then the radius of circle is

The area of a triangle with vertices A (0, 8), O (0, 0), and B (5, 0) is :

In ∆ABC, AD is the internal bisector of ∠A, meeting the side BC at D. If BD = 5 cm, BC = 7.5 cm, then AB : AC is 

An exterior angle of a regular polygon is 72^o. The sum of all the interior angles is -

In the given figure ABC is an equilateral triangle. Two circles of radius 4 cm and 12 cm are inscribed in the triangle. What is the side (in cm) of an equilateral triangle?