📐 geometry

1. **Problem Statement:** We are given a square inscribed in a smaller circle, rotated 45 degrees, with two known angles inside the square: 34° and 84°. We need to find the 5 unkno

1. **Problem statement:** We have a kite ABCD with diagonals AC and DB perpendicular at point E. Given DE = EB, AD = 8 cm, CD = 5 cm, and right angle at E, find the length of AC. 2

1. The problem is to analyze the set of points given: $\{(-6,0), (9,6), (0,-2), (-3,-5), (-6,-7), (5,7)\}$.\n\n2. Since these are discrete points, we can discuss their coordinates,

1. **State the problem:** We have a right triangle with legs of lengths 18 m and 24 m, and we want to find the length of the hypotenuse $c$. 2. **Formula used:** According to the P

1. **State the problem:** We have a right triangle with hypotenuse $45$ miles, one leg $36$ miles, and the other leg $b$ miles unknown. We need to find $b$. 2. **Formula used:** In

1. **State the problem:** We need to find the length of the hypotenuse $c$ of a right triangle where the legs are 52 mm and 39 mm. 2. **Formula used:** According to the Pythagorean

1. **State the problem:** We have a right triangle with legs of lengths 5 yards and 12 yards, and we want to find the length of the hypotenuse $c$. 2. **Formula used:** According t

1. **State the problem:** Calculate the volume $V$ of a sphere with radius $R = 9.9$ m. 2. **Formula:** The volume of a sphere is given by

1. **State the problem:** We need to find the length of the hypotenuse $c$ of a right triangle where the legs are 54 m and 72 m. 2. **Formula used:** According to the Pythagorean t

1. **State the problem:** We have a right triangle with legs of lengths 60 meters and 80 meters, and we need to find the length of the hypotenuse $c$. 2. **Formula used:** Accordin

1. **State the problem:** We are given the parametric equations of an ellipse:

1. **State the problem:** Given points and angles with various congruences and perpendicularities, prove relationships between angles and triangles using geometric theorems. 2. **G

1. **State the problem:** We are given a circle with center $(-2, 7)$ and radius $\sqrt{5}$. We need to write the equation of the circle in standard form and describe its graph.

1. **State the problem:** We have a right triangle with legs of lengths $a$ and 6 yards, and a hypotenuse of 10 yards. We need to find the perimeter, which is the sum of all three

1. **State the problem:** We have a right triangle with base $12$ cm, height $16$ cm, and hypotenuse $c$. We need to find the perimeter, which is the sum of all sides. 2. **Formula

1. **State the problem:** We have a right triangle with one leg of length 9 yards, a hypotenuse of length 15 yards, and the other leg labeled as $b$. We need to find the perimeter

1. **State the problem:** We are given a circle with center $(-6, 1)$ and radius $1$. We need to write the equation of the circle in standard form and graph it.

1. **State the problem:** We need to find the center and radius of the circle given by the equation $$(x - 3)^2 + (y + 6)^2 = 4$$. 2. **Recall the formula:** The general form of a

1. **Stating the problem:** We have a triangle inscribed in a circle with angles 67°, 9°, and an unknown angle. Outside the circle, at one vertex of an extended triangle, there is

1. **State the problem:** You drive 9 miles west, then 6 miles north. We need to find the straight-line distance from the start to the end point. 2. **Formula used:** This is a rig

1. **State the problem:** A 20-foot ladder leans against a house reaching 16 feet high. Christian pulls the base 2 feet farther from the house. We need to find the new height the l