A circle with radius 42 cm is drawn. What will be length of arc of a sector subtending an angle of 60 degrees at the Centre?

PQR is an equilateral triangle whose side is 10 cm . What is the value (in cm) of the inradius of triangle PQR ?

In any triangle ABC, AB + BC = 12 cm, BC + CA = 14 cm and CA + AB = 18 cm. What will be length of radius of a circle, if the perimeter of circle is equal to the perimeter of triangle ABC? 

P and Q are center of two circles with radii 9 cm and 2 cm respectively, where PQ = 17 cm, R is the center of another circle of radius x cm, which touches each of the above two circles externally. If ∠PRQ = 90 °, then the value of x is 

Triangle PQR is such that PQ=9 cm, QR=6 cm, PR=7.5 cm and triangle PQR is similar to triangle XYZ. If XY=18 cm, find the value of YZ.

If the ratio of the heights of two identical triangles is 4: 9, find the ratio of the areas of the two triangles.

If the circumradius of an equilateral triangle ABC is 8 cm, then what is the height of the triangle?

A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. The area of the circle is: