📐 geometry

1. **State the problem:** We need to enlarge a triangle with vertices at $(7,9)$, $(7,7)$, and $(8,7)$ by a scale factor of $-2$ with the centre of enlargement at $(6,6)$.

1. **Problem Statement:** We need to enlarge the triangle with vertices at $(2,4)$, $(2,5)$, and $(4,5)$ by a scale factor of $-3$ centered at the point $(2,3)$.

1. **Problem Statement:** We are given a triangular region in the coordinate plane with vertices at $$(2,4)$$, $$(2,5)$$, and $$(4,5)$$. We want to understand the shape and boundar

1. **State the problem:** We have a parallelogram $PQRS$ with point $P$ at coordinates $(1,1)$. Vectors are given:

1. **Problem Statement:** We need to find the measure of angle $\angle LMN$ where $M$ is a point outside circle $A$, and $ML$ and $MN$ are tangents to the circle touching points $L

1. **Problem Statement:** We need to find the measure of $\angle XYZ$ in circle $A$ given arcs $WZ = 175^\circ$ and $XZ = 105^\circ$. 2. **Relevant Formula:** The measure of an ang

1. **Problem Statement:** We need to find the perimeter of kite $OBDE$ given the circle centered at $O$, points $A, B, C, E$ on the circle, and point $D$ outside the circle. 2. **G

1. **Problem Statement:** Identify which circle has a radius measuring $10$ units. 2. **Key Concept:** The radius of a circle is the distance from the center to any point on the ci

1. **Problem Statement:** Determine the condition for a point to lie on a circle based on the distance from the center. 2. **Key Concept:** A circle is defined as the set of all po

1. **Problem Statement:** We are given a circle with center $V$ and diameter $SU$. Points $S$, $T$, and $U$ lie on the circle. The angle $\\angle SVT$ at the center $V$ is $34^\cir

1. **Problem Statement:** We are given a triangle $JKL$ with $m\angle K = 38^\circ$, side $JL = 18$, and side $JK = 8$. We need to find the measure of angle $L$ to the nearest tent

1. **State the problem:** We are given a triangle $DEF$ with $m\angle F = 61^\circ$, side $DE = 29$, and side $DF = 23$. We need to find the measure of angle $E$ to the nearest ten

1. **State the problem:** We are given a triangle $RST$ with angles $\angle S = 21^\circ$, $\angle T = 32^\circ$, and side $RT = 17$. We need to find the length of side $RS$ to the

1. **State the problem:** We are given a triangle $RST$ with angles $\angle S = 21^\circ$, $\angle T = 32^\circ$, and side $RT = 17$. We need to find the length of side $RS$ to the

1. **State the problem:** We are given a triangle $XYZ$ with angles $m\angle X = 55^\circ$, $m\angle Y = 39^\circ$, and side $YZ = 25$. We need to find the length of side $XZ$ to t

1. **State the problem:** We are given a triangle $ABC$ with angles $A = 50^\circ$, $C = 27^\circ$, and side $AB = 19$. We need to find the length of side $BC$ to the nearest tenth

1. **Problem Statement:** We have $\triangle HJK$ with points $D$, $E$, $F$ on sides $HJ$, $HK$, and $JK$ respectively. Point $G$ is the incenter of the triangle, and segments $DG$

1. **State the problem:** We need to find the volume of a sphere with radius $r = \frac{1}{2}$. 2. **Formula for the volume of a sphere:**

1. **Problem Statement:**\nWe have a semicircle with radius $r$. We need to find:\n- The diameter of the circle in terms of $r$.\n- The length of the semicircular arc in terms of $

1. **Problem Statement:** We have a composite figure made up of 3 identical triangles. The figure's left vertical side measures $30$ cm and the bottom horizontal side measures $20$

1. **State the problem:** We are given two adjacent angles formed by intersecting lines: one angle is $3x^\circ$ and the other is $(2x + 16)^\circ$. We need to find the value of $x