Z7-I-5 MO 2017
Prokop constructed a triangle ABC whose interior angle at vertex A was greater than 60° and whose interior angle at vertex B was less than 60°. Juraj drew, in the half-plane determined by line AB and point C, a point D such that triangle ABD was equilateral. The boys then found that triangles ACD and BCD are isosceles with apex vertex D. Determine the measure of angle ACB.
Final Answer:
Tips for related online calculators
Do you have a linear equation or system of equations and are looking for its solution? Or do you have a quadratic equation?
Calculation of an isosceles triangle.
Calculation of an equilateral triangle.
See also our trigonometric triangle calculator.
Calculation of an isosceles triangle.
Calculation of an equilateral triangle.
See also our trigonometric triangle calculator.
You need to know the following knowledge to solve this word math problem:
geometryalgebraplanimetricsUnits of physical quantitiesthemes, topicsGrade of the word problem
We encourage you to watch this tutorial video on this math problem: video1
Related math problems and questions:
- Triangle angle operations
There are also two equilateral triangles ABC, and BDE, such that the size of the angle ABD is greater than 120° and less than 180° points C and E lie in the same half-plane defined by the line AD. The intersection of CD and AE is marked F. Determine the s - Maturitný - RR - base
In an isosceles triangle ABC with base AB, ∠BAC = 20°, AB = 4. The axis of the interior angle at vertex B intersects side AC at point P. Calculate the length of the segment AP. Give the result to two decimal places. - In plane 2
A triangle ABC is located in the plane with a right angle at vertex C, for which the following holds: A(1, 2), B(5, 2), C(x, x+1), where x > -1. a) determine the value of x b) determine the coordinates of point M, which is the midpoint of line segment - Rectangular trapezoid
The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate the trapezium area in cm square and calculate how many different perimeters - Internal angles
The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On the BC side is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA, the point M is such that | DM | = 2 |MA|. Det - MO Z7–I–6 2021
In triangle ABC, point D lies on the AC side and point E on the BC side. The sizes of the angles ABD, BAE, CAE, and CBD are 30°, 60°, 20°, and 30°, respectively. Find the size of the AED angle. - Right angle
In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
