# Inscribed angle theorem - math word problems

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 circle#### Number of problems found: 15

- Interior angles

In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles. - Hexagon in circle

Calculate the radius of a circle whose length is 10 cm greater than the circumference of a regular hexagon inscribed in this circle. - Clock hands

Calculate the internal angles of a triangle whose vertices lie on the clock's 2, 6 and 11 hours. - Dodecagon

Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees. - Diagonals

Draw a square ABCD whose diagonals have a length of 6 cm - Diagonal in rectangle

In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts. - Circular segment

Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm and the angle α = 60°. Help formula: S = 1/2 r2. (Β-sinβ) - 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. - 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 legs. - Inscribed circle

Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC. - Clock face

clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles. - Circumferential angle

Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 2:2:9. Determine the size of the angles of the triangle ΔABC. - Circular pool

The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool? - 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. - Circle arc

Circle segment has a circumference of 135.26 dm and 2096.58 dm^{2}area. Calculate the radius of the circle and size of central angle.

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