Practice problems of the inscribed angle theorem - last page
The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle. An inscribed angle is the angle formed in the interior of a circle when two secant lines intersect on the circleDirection: Solve each problem carefully and show your solution in each item.
Number of problems found: 53
- 6 regular polygon
A regular six-sided polygon has a side 5 cm long. Calculate its area. Compare how many more cm² (square centimeters) has a circle inscribed the 6-gon. - Complete construction
Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of the legs. - Diagonal in rectangle
In the ABCD rectangle is the center of BC, point E, and point F is the center of the CD. Prove that the lines AE and AF divide diagonal BD into three equal parts. - Pentagon
Within a regular pentagon ABCDE point, P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
- Circular pool
The pool's base is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length of 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool? - Clock face
A clock face is drawn on paper. Straight lines connect numbers 10 and 5 and 3 and 8. Calculate the size of their angles. - Inscribed triangle
To a circle is an inscribed triangle so that it is vertexes divide the circle into three arcs. The length of the arcs is in the ratio 2:3:7. Find the interior angles of a triangle. - The chord
A chord passing through its center is the side of the triangle inscribed in a circle. What size are the internal angles of a triangle if one of them is 40°? - Circle section
An equilateral triangle with side 33 is an inscribed circle section whose center is in one of the triangle's vertices, and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio between the circumference to the circle sector a
- Semicircle
The semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC? - Circumferential angle
Vertices of the triangle ΔABC lay on the circle and are divided into arcs in the ratio 7:8:7. Determine the size of the angles of the triangle ΔABC. - Circle arc
The circle segment has a circumference of 135.26 dm and 2096.58 dm² area. Calculate the radius of the circle and the size of the central angle. - Isosceles trapezium
Trapezoid YUEB (YU||EB) is isosceles. The size of the angle at vertex U is 49 degrees. Calculate the size of the angle at vertex B.
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