Rectangle and Semicircles

In the given figure, four equal semicircles are placed in a rectangle ABCD. Each of diameters AD, EF, BC and GH is 4 cm . 

What is the area of the region shaded in yellow ?

 

Semicircle

In the given figure, AC is the diameter of the semicircle with center O. B is a point on the semicircle such that area of the triangle ABC is 24 sq.cm . Incircle of triangle ABC touches AC at point D. DO = 1 cm .

What is the area of the Incircle ?

 

Trapezium and Circle

In the given figure, ABCD is a Trapezium. AB is parallel with DC. Each of angle BAD and ADC is 90 degree. Incircle EFGH touches AB, BC, CD and DA at points E, F, G and H respectively. 

Triangle and Circles

 

In the given figure, ABC is a right angle triangle, right angle at B, BD is perpendicular to AC. MNP is incircle of triangle ABC touches AC at M. O is the center of the incircle. Inradius OM = 15 cm .  AC is tangent to the bigger circle at point D and the center is at B. Bigger circle intersects AB at point E and BC at point F.  FC = 9 cm and AE = 24 cm .

What is the area of the triangle ABC ?

Rectangle

 In the given figure, ABCD is a rectangle. AC is tangent to two equal circles.     AC = 65 cm and MN = 23 cm.

What is the area of the Rectangle ABCD ? 

Trapezium

In the given figure, Trapezium ABCD is circumscribed, touching the circle at P, Q, R and S.AB is parallel with DC. ADC is right angle. PB = 10 cm. Radius OR = 50 cm. 

What is the area of the Trapezium ?

Rhombus

ABCD is  a Rhombus. A Circle through vertex A and C intersects AB at point E and CD at point F. EB = 119 cm and EF = 130 cm . What is the area of the rhombus ?

PARALLELOGRAM

 ABCD is a parallelogram in which   AB - BC = AC - BD . Perimeter of the 

parallelogram is 48 cm . 

What is the length of the smaller side ?