📐 geometry

1. **Problem statement:** Given a circle with diameter $\overline{AB}$, find the sizes of the angles: a) $\angle ABP$

1. Let's state the problem: We want to find the volume of a triangular prism. 2. The volume $V$ of a prism is given by the formula:

1. **State the problem:** We need to find the length of segment $PH$ where $P$ is a vertex of the rectangular base PQRS and $H$ is the midpoint of the top edge $FG$ of the wedge. G

1. **Problem statement:** We have a circle with an inscribed angle measuring 26°. A tangent touches the circle at the endpoint of the chord forming an angle $x$° with the chord out

1. The problem states that the sum of two angles $x$ and $y$ is given by $x + y = \frac{320}{3}^\circ \approx 106.67^\circ$.\n\n2. We are to understand or analyze the relationship

1. The problem is to find the volume of a cone. 2. The formula for the volume of a cone is given by

1. The problem states that there is a circle centered at point B, with points A, C, and D on the circumference. 2. Given that $\angle ABC = 40^\circ$, we need to find the measure o

1. **Problem Restatement:** We have a circle centered at point B with points A, C, and D on the circumference. 2. **Given:** $\angle ABC = 40^\circ$.

1. **Problem statement:** Given a circle with diameter $AB$, we need to find the sizes of angles $\angle A\hat{B}P$, $\angle A\hat{B}Z$, $\angle A\hat{Y}Z$, $\angle B\hat{Y}Z$, $\a

1. Problem: Find the missing lengths in circle M given BD = 3, KM = 6, KP = 2\sqrt{7}, and some segment lengths. 2. Given AP = 2\sqrt{7} and CD = 3, we look to find AK, MD, AM, DS,

1. The problem asks to explain the concept of slant height in a right square pyramid. 2. A right square pyramid has a square base and an apex directly above the center of the base,

1. The problem involves filling in blanks about directions and turns on a 4-point compass. 2. From the graph description: N is labeled at the right, so (h) N is right.

1. The problem provides definitions: radius = line from circle center to a point on circle; chord = line connecting two points on circle; diameter = chord through center with lengt

1. Problem: Find missing lengths in circle M with given segments BD=3, KM=6, KP=2\sqrt{7}. Find AP, CD, AK, MD, AM, DS, KL, MP. 2. Problem: Radius OB \perp AC at G. Given various l

1. The problem involves plotting given points on two Cartesian planes with different scales. 2. For the first Cartesian plane, the scale is 1 cm representing 5 units for both x and

1. **Stating the problem:** We have parallelogram ABCD with \(\angle DAB = 122^\circ\) and point E on side DC such that \(\angle EBC = 22^\circ\).

1. Filling in the blanks for compass directions relative to point P: (g) R is south-east of P.

1. **Énoncé du problème :** Nous avons le segment ST défini par l'équation $y = -\frac{1}{2}x + 300$.

1. Let's start by understanding the problem. You have a circle with points M, D, and a line from B intersecting at points x and y.

1. **Énoncé du problème :** Calculer la longueur des arcs de deux formes géométriques : un demi-cercle et un quart de cercle.

1. Problem: Identify angle relationships in given figures with parallel lines and transversals. 2. Identify corresponding angles (4 pairs):