Area of a Circle: Using Pythagoras' theorem

The center of the circle in the figure below is O.

AB is perpendicular to BC.

BC = 12

AC = 13

Calculate the area of the circle.

$6.25\pi$

From the point O on the circle we take the radius to the point D on the circle. Given the lengths of the sides in cm:

DC=8 AE=3 OK=3 EK=6

EK is perpendicular to DC

Calculate the area between the circle and the trapezoid (the empty area).

36.54

The trapezoid ABCD is drawn inside a circle.

The radius can be drawn from point O to point C.

DC = 12 cm
OK = 3 cm
NB = 4 cm
NK = 5 cm

Calculate the white area between the trapezoid and the circle's edge.

91.37

ABC is a right-angled triangle.

AB is perpendicular to BC.

O1 and O2 are identical and are located on AC in such a way that they are tangent to each other as shown in the diagram.

AB=4

BC=3

What is the area of O1 and O2?

$\frac{25}{16}\pi$ cm²

Triangle ABC given in the drawing is isosceles, AB=AC

AD is perpendicular to BC

The circle whose diameter is AC is $13\pi$ cm

For side DC, a semicircle whose area is cm² is placed

What is the area of the triangle?

60 cm²