Triangle and Circle

 

Rectangle and Circles

In the given figure ABCD is a rectangle. E is point on AB such that incircle of triangle EBC touches EB, BC, and EC at point M, N and P respectively. OM = 2 cm . Bigger Circle touches AE, EC, DC and AD at points R, S, U and T respectively. G and F are two points on AD and H is a point on DC. EF and GH intersects at point Q, such that angle GQE is 90 degree. AE = AF.

What is the area of the rectangle? 

Rectangle and Circles

In the given figure, ABCD is a rectangle. E is a point on AB such that inradius OF of incircle of triangle EBC is 4 cm. Bigger circle touches AE,EC,DC and AD at points J,K,L and I respectively. JE =1cm.

What is the area of the bigger circle ?

 

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 ?

 

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 ?

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 ?