📐 geometry

1. **Problem statement:** We have an oval track ABCD with given lengths |AB| = 20 cm and |BC| = 14 cm. We need to calculate: (i) The perimeter of the track.

1. **Problem statement:** We have an equilateral triangle with side length $x$ and a right triangle inside it where one leg is $\sqrt{10}$ and the other leg is $x$. We need to find

1. **State the problem:** We need to find the length of side $x$ in a triangle with angles $30^\circ$, $60^\circ$, and the side opposite $60^\circ$ is $\sqrt{7}$. 2. **Identify the

1. Let's analyze the lines of symmetry (LoS) for each shape based on their properties and descriptions. 2. **Square:** Has 4 equal sides and right angles. It has symmetry lines thr

1. **Problem Statement:** Illustrate the given Euclidean geometry concepts about points, lines, angles, and triangles.

1. The problem involves understanding and illustrating key differences between Euclidean and spherical geometry concepts. 2. In Euclidean geometry, two given collinear points deter

1. The problem states that triangles \(\triangle MJL\) and \(\triangle KNL\) are similar, denoted as \(\triangle MJL \sim \triangle KNL\). We need to identify pairs of congruent an

1. **State the problem:** We are given a circle with center D, radius 14 inches, and a sector formed by points E and F with central angle $\angle EDF = 48^\circ$. We need to find t

1. **State the problem:** Rowan wants to enlarge a shape using the origin $O$ as the center. The ratio of the length $OA$ to $OA'$ is $2:1$. Given $A(5,6)$, find both possible coor

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: