📐 geometry

1. The problem is to find the missing base of a trapezium given the area, one base, and the height. 2. The formula for the area of a trapezium is:

1. **Problem statement:** Given an acute triangle ABC inscribed in a circle with center O. The altitudes BM and CN intersect at H and meet the circle again at points E and F respec

1. **State the problem:** We need to find the lateral surface area of a regular quadrilateral pyramid with a base perimeter of 40 cm and a height of 12 cm. 2. **Identify the base s

1. **State the problem:** Find the number of planes that pass through three non-collinear points. 2. **Recall the geometric rule:** Through any three points that are not on the sam

1. **Stel het probleem vast:** We hebben een gebroken glasvorm met verschillende zijden en we willen de lengte van de verticale zijde rechts vinden, aangeduid met een vraagteken. 2

1. **State the problem:** We have a rectangle with length 15 m and width 2 1/3 m. We need to find: a) An estimate for the area.

1. **Énoncé du problème :** On a un triangle ABC avec $AC=6$, $AB=3$ et l'angle $\angle A = \frac{\pi}{6}$.

1. Bài toán: Tìm phương trình đường tròn cơ bản với tâm $I(h,k)$ và bán kính $r$. 2. Công thức đường tròn: $$ (x - h)^2 + (y - k)^2 = r^2 $$

1. **Stating the problem:** We are given a right triangle with vertical side AB of height $1.6 + 25 = 26.6$ meters, and angle $\angle ACB = 38^\circ$ between the diagonal AC and th

1. **Problem statement:** The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to the base is 3 : 2. Using Heron's formula, find the area of the triangle. 2

1. **Problem statement:** We have a right triangle with a vertical height labeled $h$, a base segment labeled $x$, and given side lengths: the left vertical side is 65, the top hor

1. نبدأ ببيان المشكلة: لدينا دائرة مركزها النقطة $ (5, -3) $ وتلامس محور السينات (محور $x$). نريد إيجاد معادلة هذه الدائرة. 2. معادلة الدائرة العامة هي:

1. The problem asks to find 5 squares shaded on a 3x3 grid numbered 1 to 9 such that the pattern has 4 lines of symmetry. 2. The 4 lines of symmetry in a square grid are: vertical,

1. **State the problem:** We need to find the order of rotational symmetry of a 5x5 grid pattern with grey squares at positions (1,2), (1,4), (2,3), (3,2), (3,4), (4,2), and (4,4).

1. The problem involves comparing two similar triangles and their corresponding side lengths. 2. Similar triangles have proportional sides, meaning the ratios of corresponding side

1. **State the problem:** We have two similar pentagons ABCDE and RSTUV. We know some side lengths of ABCDE and one side length of RSTUV (TU = 33 cm). We need to find the length of

1. **Circle Theorem Problem:** State the problem: In circle $O$, chord $AB$ subtends an angle of $40^\circ$ at point $C$ on the circumference. Find the angle subtended by the same

1. **Problem statement:** In a circle with center O, points A, B, C, and D lie on the circumference. Chord AB is drawn and angle ACB is formed at point C on the circle. Given that

1. The problem states two scenarios involving quadrilateral ABCD with given angles and parallel lines. 2. We will solve the first scenario: AB || DC, \(\angle BDC = 35^\circ\), and

1. **Problem Statement:** Find the value of $x$ in the parallelogram $ABCD$ where angle $B$ is $34^\circ$ and angle $D$ is $x$.

1. The problem shows a parallelogram ABCD with sides AB and CD opposite each other, and sides AD and BC opposite each other. 2. In a parallelogram, opposite sides are equal in leng