In ΔABC, ∠C=90° and D is a point on CB such that AD is the bisector of ∠A. If AC=5 cm and BC=12 cm, then what is the length of AD?

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

If the area of a circle, inscribed in a equilateral triangle is 4 π cm², then what is the area of the triangle?

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?

If there are four lines in a plane, then what cannot be the number of points of intersection of these lines? 

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:

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?