📐 geometry

1. The problem asks for the coordinates of the midpoint of the line segment OE, where O is at (0,0) and E is at (14,22). 2. The formula for the midpoint $M$ of a segment with endpo

1. **State the problem:** We need to find the coordinates of point M, which is the midpoint of the line segment CD. 2. **Formula for midpoint:** The midpoint M of a segment with en

1. **Problem statement:** We are given the center of a circle at point $C(2,1)$ and a point on the circle $P(8,9)$. We need to find:

1. **Problem Statement:** Given two overlapping circles with points A, B on the larger circle and points D, O on the smaller circle, and given angles 90° at D, 42°, 30°, and 120°,

1. **Problem statement:** Given a cone with radius $r = x$ and height $h = 4x$, prove that its volume is $\frac{4}{3}\pi x^3$. 2. **Formula for volume of a cone:**

1. **State the problem:** We need to find the volume of water in the trough when the water depth is three quarters of the height of the trough. 2. **Given dimensions:** Length = 1.

1. **Stating the problem:** We are given a right triangle with sides BC = 5 inches, CD = 5 inches, and AD = 13 inches. We need to find the length of side AB in centimeters, knowing

1. **Problem Statement:** Calculate the total surface area of a frustum of a right pyramid with rectangular base ABCD where $AB=32$ cm, $BC=24$ cm. The top face EFGH is parallel to

1. **State the problem:** Calculate the total surface area of the frustum formed by cutting a right pyramid ABCD with a plane EXOH parallel to the base. 2. **Given data:**

1. **Énoncé du problème 23** : Trace un triangle ABC. Place D et E les milieux respectifs de [AB] et [BC]. Place un point F sur [AC], tel que la distance d(F, E) = d(F, E) (probabl

1. The problem asks to find the length of a cube given its volume is 3375 cm³. 2. The formula for the volume of a cube is $$V = s^3$$ where $s$ is the length of a side.

1. **Problem statement:** We have an equilateral triangle $\triangle ABC$ and a square $DEFG$ inscribed inside it such that $D$ lies on $AB$, $E$ on $BC$, and $F$ on $AC$. Lines $A

1. Stating the problem for Day 4: Given quadrilateral ABEDC with triangles ABE and DEC, determine the nature of these triangles, show that angle AÊB = 70°, and deduce the measure o

1. **Problem statement:** Calculate the volume of the part of the cone that is not in contact with water when a conical solid of radius 14 cm is fitted into a cylindrical tin of ra

1. **Problem Statement:** ABCD is a rhombus where the altitude from vertex D to side AB bisects AB. We need to find the angles of the rhombus. 2. **Understanding the problem:** A r

1. **Problem Statement:** Given triangle ABC, right-angled at B, and D is the midpoint of AC. We need to prove that $DA = DB = DC$. 2. **Understanding the problem:** Since $D$ is t

1. **Problem Statement:** Calculate the total volume of units 1 to 15, each with a height of 3 meters. 2. **Given Data:** Each unit has a floor area defined by the floor plan. The

1. **Stating the problem:** We need to find the angle $x$ in a quadrilateral with given angles $100^\circ$ and $126^\circ$ and two pairs of equal sides. 2. **Understanding the prop

1. **Đề bài:** Cho tam giác vuông $\triangle ABC$ vuông tại $A$. Qua điểm $C$ kẻ đường thẳng $d$ vuông góc với $AC$. Trên $d$ lấy điểm $E$ sao cho $CE=AB$ và $E$, $B$ thuộc hai nửa

1. ସମସ୍ୟା କହାଯାଇଛି: ଏକ ବୃତ୍ତର ବ୍ୟାସାର୍ଦ୍ଧ $15$ ସେମି ଓ ଏକ ଜ୍ୟାର ଦୈର୍ଘ୍ୟ $24$ ସେମି ଦିଆଯାଇଛି। 2. ବୃତ୍ତର ବ୍ୟାସାର୍ଦ୍ଧ ହେଉଛି ବ୍ୟାସ $d=15$ ସେମି, ତେଣୁ ବୃତ୍ତର ତ୍ରିଜ୍ୟା $r=\frac{d}{2}=\frac{

1. **Problem statement:** We have a semicircle PQRS with center O and radius $r$. The semicircle is divided into three arcs of equal length by points P, Q, R, and S. We need to fin