📐 geometry

1. **State the problem:** We are given a sphere and a cone. The surface area of the sphere equals the curved surface area of the cone. We need to find the slant height $l$ of the c

1. **State the problem:** We have a sphere and a cone with the same curved surface area. The sphere has radius $3y$ and the cone has radius $3y$ and slant height $l$. We need to:

1. **Énoncé du problème :** Soit un triangle ABC avec un point I tel que $\overrightarrow{AI} = -\frac{4}{2} \overrightarrow{AB} = -2 \overrightarrow{AB}$. On définit le barycentre

1. The problem states that Thimo is standing on the northeast side of the building. 2. Northeast means the direction that is between north and east, typically the top-right corner

1. **Problem Statement:** A farmer wants to divide a triangular field into four equal smaller triangles using fences. We need to use the midline theorem to determine where to place

1. **Nêu bài toán:** Cho tam giác đều ABC cạnh 6m. Cần tìm hình chữ nhật MNPQ với M, N trên BC, P trên AC, Q trên AB sao cho diện tích hình chữ nhật lớn nhất.

1. **Problem statement:** We have a quadrilateral ABCD with angles $\angle A = 60^\circ$ and $\angle B = 50^\circ$. We need to find the measures of angles $\angle C$ and $\angle D$

1. The problem states that we have a parallelogram with one angle measuring 68° and we need to find the other three angles labeled $x$, $y$, and $z$. 2. Important properties of par

1. The problem is to prove that the sum of the interior angles of a triangle is 180 degrees. 2. According to the Midpoint Line Theorem (MDLB theorem), a line drawn through the midp

1. **State the problem:** We are given a right triangle with vertices W, X, Y, and Z, where the right angle is at vertex W. The lengths of segments YW and XZ are given as expressio

1. مسئله: محیط و مساحت مثلث متساوی الاضلاع برابرند و مساحت 30 است. ارتفاع مثلث را بیابید. 2. فرمول مساحت مثلث متساوی الاضلاع با ضلع $a$:

1. Problem statement: In the figure, \overline{AD} and \overline{CE} are diameters of circle $P$.

1. **Problem statement:** We are given a circle with diameters AD and CE intersecting at center P. We need to find the measure of the minor arc AB in degrees. 2. **Key information:

1. பிரச்சினையை விளக்குக: ஒரு உருண்ட வடிவான பாத்திரத்தின் அடியின் பரிதி $10.5$ செ.மீ. மற்றும் உயரம் $20$ செ.மீ. உள்ளது. அதன் மேல்மேற்பரப்பின் பரப்பளவை காண வேண்டும். 2. மேல்மேற்பரப்ப

1. Given a circle with circumference $44$ cm, find the radius $r$ using the formula for circumference: $$C=2\pi r$$

1. Given a triangle with angles 40°, 100°, and $x$ degrees, we need to find the value of $x$. 2. Recall the rule that the sum of the interior angles of any triangle is always 180°.

1. نبدأ ببيان المسألة: لدينا متوازي سطوح بأحرف متجاورة م، ب، ج، حيث \( \vec{م} \times \vec{ج} = 2\vec{س} - \vec{ص} + \vec{ع} \) وجيوب تمام اتجاه ب هي \( (\frac{1}{7}, 0, 0) \) و \(

1. نبدأ ببيان المشكلة: لدينا متوازي سطوح أ ب ج، مع متجهات متجاورة م→× = ٧ س – ص + ٤ ج، وجيوب تمام اتجاه ب ك هي ( ١/٧، ٠، ٠) و ( ١/٧، ١/٧، ٠). المطلوب هو إيجاد حجم متوازي السطوح إذا

1. **Problem:** Given the previous problem context, solve the next question labeled as 23 (assuming it is a separate problem). Since the user did not provide the details of questio

1. **Problem:** In the figure, given $\angle SPR = 73^\circ$ and $\angle SRP = 42^\circ$, find $\angle PQR$. 2. **Step 1: Understand the triangle SPR**

1. **Problem:** Draw an angle and label it as $\angle BAC$. Construct another angle equal to $\angle BAC$. 2. **Formula and rules:** To construct an angle equal to a given angle, w