If in a triangle, the orthocenter lies on vertex, then the triangle is 

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 

Find the second diagonal of a rhombus when it’s first diagonal length is 12 cm and its side is 10 cm?

A secant PAB is drawn from an external point P to the circle with centre O, intersecting it at A and B. If OP = 17 cm, PA = 12 cm and PB = 22.5 cm, then the radius of the circle is:

AB is diameter of a circle with centre 'O'. CD is a chord which is equal to the radius of the circle. AC and BD are extended so that they intersect each other at point P. Then find the value of ∠ APB.

ΔABC is similar to ΔDEF. Length of AB is 18 cm and  length of the corresponding side  DE is 10 cm. What is the ratio  of Perimeter of ΔABC : Perimeter of ΔDEF?

ΔABC and ΔDBC are on the same base BC but on opposite sides of it. AD and BC intersect each other O. If AO=a cm, DO=b cm and the area of ΔABC= x cm², then what is the area (in cm²) of ΔDBC?

ABCD is a rhombus whose one angle is 60°.Find the ratio of the lengths of its diagonal?