Circles in Plane Geometry

Geometry Quiz

 













Question 1: Triangle ABC in the figure below is inscribed in circle C of center O. Suppose D is the midpoint of segment AC and E is the midpoint of segment BC. What is the area of the circle if the segment OD measures 3 cm?















Question 2: Two diameters of a circle create ∠AOB of 45o between them. What is the length of arc AB if the radius of the circle is 16?











Question 3: If side a of triangle ABO is tangent to the circle of center O, what is the value of the side b in mm? Side a of the ABO triangle is 40mm and the radius of the circle is 30mm.














Question 4: Calculate the ratio between the area of circle C of center O and the area of the square ABCD in the figure below:














Question 5: A circle of radius r and center O is inscribed in a right isosceles triangle ABC. Calculate the relation between the cathetus AB and the radius of the circle.




















Question 6: Two congruent circles with the centers in A and C intersect each other in points B and D. The geometric figure ABCD is a:













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