ΔABC is an equilateral triangle in which D, E and F are the points on sides BC, AC and AB, respectively, such that AD ⊥ BC, BE ⊥ AC and CF ⊥ AB. Which of the following is true?

A unique circle can always be drawn through x number of given non-collinear points, then X must be 

PQR is a right angled triangle in which PQ = QR . If the hypotenuse of the triangle is 20 cm , then what is the area ( in cm ) of the triangle PQR ?

The area enclosed between the circumferences of two concentric circles is 45π square cm and their radii are in the ratio of 3:2. What is the area off the outer circle?

If the sum of the interior angles of a regular polygon be 1080 °, the number of sides of the polygon is 

Given that (a²+b²)=60, then find the value of (a+b)²+(a–b)².

Each internal angle of regular polygon is two times its external angle. Then the number of sides of the polygon is: 

A line touches a circle of a radius 6 cm. Another line is drawn which is tangent to the circle. If the two lines are parallel then the distance between them is: