📐 geometry

1. **Problem statement:** We have a pyramid with apex $P$ and rectangular base $ABCD$ where $PA=PB=PC=PD$. The base edges are $DC=13$, $CB=27$, and $AB=16$ cm. We need to find the

1. **Problem statement:** We have a pyramid with apex $P$ and rectangular base $ABCD$. The edges $PA = PB = PC = PD$ are equal. The base sides are $DC = 13$, $CB = 27$, and $AB = 1

1. **المشكلة:** أوجد محيط المثلث (أ ب ج) حيث نصف أقطار الدوائر أ=3، ب=2، ج=1. 2. **المعطيات:** نصف قطر الدائرة أ = 3، نصف قطر الدائرة ب = 2، نصف قطر الدائرة ج = 1.

1. **Problem Statement:** We have a cyclic quadrilateral inscribed in a circle with two pairs of equal sides. One interior angle at the bottom right corner is $38^\circ$, and an ex

1. **Problem 1: Find the slant height $s$ of the square-based pyramid.** Given:

1. **Problem Statement:** Prove that in a circle with center O and diameter AB, the angle at the circumference subtended by AB is a right angle, i.e., $\angle ARB = 90^\circ$. 2. *

1. **State the problem:** We need to solve for side $c$ in a triangle using the Law of Cosines. 2. **Law of Cosines formula:**

1. **Problem statement:** We have a circle with center $O$. Segments $UX$ and $UV$ are tangents to the circle, and $XV$ passes through the center $O$. Given $UV=12.6$ and $XV=12$,

1. The problem is to find the length of the hypotenuse or a missing side in a right triangle using the Pythagorean theorem. 2. The Pythagorean theorem states that in a right triang

1. **Problem Statement:** We have a circle centered at $O$ with tangent segments $\overline{EH}$ and $\overline{EF}$ from point $E$ to the circle. The segment $\overline{HF}$ passe

1. The problem is to create a practice test based on Alberta Grade Nine Circle Geometry. 2. Circle geometry involves properties and theorems related to circles, such as angles, cho

1. **Problem statement:** Determine the values of $d^\circ$, $e$, and $f$ for the given circles with center $O$. 2. **Key circle property:** The angle subtended at the center of a

1. **Stating the problem:** We are given angles \(\angle BAD = (2a + 25)^\circ\) and \(\angle BCD = (3a - 15)^\circ\). We need to find: a. The value of \(a\)

1. **Problem Statement:** We have a parallelogram ABCD with sides given as: - AB = $3x - 5$ cm

1. **State the problem:** Calculate the area of the composite shape that looks like a right-pointing arrow with given dimensions: height 6 ft on the left, width 7 ft at the bottom,

1. **Problem Statement:** We are given triangle L M N with vertices approximately at $L(2,2)$, $M(5,6)$, and $N(6,3)$, and its image triangle L' M' N' with vertices approximately a

1. **State the problem:** Determine if triangles \(\triangle JKL\) and \(\triangle MNP\) are similar, and if so, identify the correct similarity criterion. 2. **Given data:**

1. **Problem statement:** We have triangle $\triangle LMN$ with vertices $L(2,2)$, $M(6,6)$, $N(6,2)$ and its image $\triangle L'M'N'$ with vertices $L'(11,2)$, $M'(7,6)$, $N'(7,2)

1. **State the problem:** We have a rectangle with width $14x$ and height $y$. There are two shaded strips: one at the top with height $x - 8$ and one on the right side with width

1. **Problem:** Find the unknown angle at vertex R in parallelogram RQST where angle at S is 135°. 2. **Formula and rules:** In a parallelogram, opposite angles are equal, and adja

1. **State the problem:** We are given the circumference of a circle as 165 mm and need to find the area of the circle, rounded to 1 decimal place. 2. **Recall the formulas:**