Right triangle + Euclid's theorems - practice problems - last page
Number of problems found: 56
- Touch circle
Point A has a distance (A, k) = 10 cm from a circle k with radius r = 4 cm and center S. Calculate: a) the distance of point A from the point of contact T if the tangent to the circle is drawn from point A b) the distance of the contact point T from the l - Tangents
From point R, two tangents are drawn to a circle with a radius of 41 cm. The distance between the two points of tangency is 16 cm. Calculate the distance from point R to the centre of the circle. - The bridge
Across the circle, the lake passes through its center bridge over the lake. At three different locations on the lakeshore are three fishermen, A, B, and C. Which of the fishermen sees the bridge from the largest angle? - Isosceles IV
In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle. - RRL Basics
What is the length of the smaller base and the height of an isosceles trapezoid if a = 9 dm, the leg is 6 dm, and angle ACB = 90°? - Right isosceles triangle
The right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse, dividing it into two equal segments. One segment is 5 cm long. What is the area of the triangle? - Right 24 The right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse, dividing it into two unequal segments. One segment is 5 cm long. What is the area of the triangle? Thank you.
- Right triangle area
In a right-angled triangle ABC, the height of side c has a length of 6 cm. The letter D indicates the heel of the height. Line segment AD is 8 cm long. Calculate the area of triangle ABC. ( example on Monitor 9 ) - Construction - Euclid
Using Euclid's theorems, construct a triangle ABC with height on side c and size v = √8 cm. Choose the length of the hypotenuse c correctly. Write the construction procedure. - Triangle circle calculation
The following elements are known in the right triangle ABC: a = 10 cm, height to side c h = 9.23 cm. Calculate o, R (radius of the inscribed circle), r (radius of the inscribed circle). - Triangle calculation complete
Calculate the right triangle ABC, the perpendicular b = 43.5 cm of the hypotenuse c = 72.9 cm. Calculate: A hypotenuse segment cb, side a, a hypotenuse segment ca, and a height of triangle v - Same area
There is a given triangle. Construct a square of the same area. - Rhombus
A rhombus has a side length of a = 20 cm. The points where the inscribed circle touches the sides divide each side into segments of length a₁ = 13 cm and a₂ = 7 cm. Calculate the radius r of the inscribed circle and the lengths of the diagonals of the rho - Quadrilateral circle radius
Given is a quadrilateral ABCD inscribed in a circle, with the diagonal AC being the circle's diameter. The distance between point B and the diameter is 15 cm, and between point D and the diameter is 18 cm. Calculate the radius of the circle and the perime - Goat and circles
What is the radius of a circle centered on the other circle, and is the intersection of the two circles equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which - Square equal rhombus
Construct a square that has the same area as a rhombus ABCD if |AB| = 5 cm, |AD| = 4 cm, and angle |DAB| = 30°.
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