📐 geometry

1. مسئله را بیان می‌کنیم: الف) طول میانه AM در مثلث با رئوس A(4,2)، B(-3,2) و C(-1,1) را بیابید.

1. مسئله: نقاط A(2,4) و B(-3,2) و C(1,-2) رأس‌های یک مثلث هستند. الف) طول میانه AM را بیابید. 2. تعریف میانه: میانه از راس A خطی است که به وسط ضلع مقابل (BC) وصل می‌شود. ابتدا مختص

1. **Problem Statement:** If the height of a cylinder is increased by 15% and the radius of its base is reduced by 10%, find the percentage change in the surface area of the cylind

1. **State the problem:** We need to find the size of angle $ABC$ to the nearest degree. 2. **Analyze the given information:** Point $B$ is at the center of the protractor baseline

1. The problem asks for the size of angle ABC, where points A, B, and C lie on a semicircular protractor. 2. Point B is at 0 degrees on the flat edge, point A is at 180 degrees, an

1. The problem asks for the length of the altitude $n$ of an equilateral triangle with side length 6. 2. In an equilateral triangle, all sides are equal, and the altitude splits th

1. **Problem statement:** We have a right triangle with angles 45°, 45°, and 90°. One leg length is 4, the hypotenuse length is $\sqrt{32}$, and the other leg length is $s$. We nee

1. The problem asks to find the values of angles A, B, C, and D in the given geometric figures. 2. Since the user did not specify which figure or provide specific angle relationshi

1. **State the problem:** We need to find the circumference of a circle with a diameter of 18 yards. 2. **Formula:** The circumference $C$ of a circle is given by the formula:

1. **State the problem:** We need to find the circumference of a circle with a diameter of 18 yards. 2. **Formula:** The circumference $C$ of a circle is given by the formula:

1. **Problem Statement:** Nakul has a cylindrical container of volume 3080 cm³, half filled with water. When a spherical ball is dropped in, the water level rises, increasing the v

1. **Problem Statement:** Calculate the radius of a sphere if its volume is 904.32 cm³. 2. **Formula Used:** The volume $V$ of a sphere is given by the formula:

1. **Problem statement:** Find the bearing of point B from point A given that the angle between the north line at A and the line AB is 53° to the west of north. 2. **Understanding

1. **State the problem:** We need to find the bearing of point B from point A given that the angle between the north line at A and the line from A to B is 53° to the left (west) of

1. **Problem Statement:** We have two similar pentagons QRSTU and HGFEI. Given some side lengths, we need to find the lengths of RS and HI. 2. **Given Data:**

1. **Problem statement:** We are given the offset distance from PC (Point of Curvature) to PT (Point of Tangency) of a simple curve as 8 meters, and the length of the curve as 60 m

1. **Problem statement:** We have a line 𝓛 defined by parametric equations:

1. **Problem:** Find the missing angle or side length in a rhombus given algebraic expressions. 2. **Important properties of a rhombus:**

1. Bài toán: Cho đường tròn tâm $O$, đường kính $AB$. Kẻ tiếp tuyến tại $B$ với đường tròn $(O)$, trên tiếp tuyến lấy điểm $P$. Qua $A$ kẻ đường thẳng song song với $OP$ cắt đường

1. **Stating the problem:** We are given a triangle ABC with points D and E on sides AC and AB respectively, and segments BD, BE, and EA inside the triangle. The side lengths AB=11

1. مسئله: در مثلث ABC، خط BD نیمساز زاویه B است و در مثلث BDE، ارتفاع بر ضلع BE موازی ضلع BC است. باید طول EA را پیدا کنیم. 2. داده‌ها: AB=11، BC=8، BD نیمساز زاویه B است.