📐 geometry

1. **Find the length of the segment indicated in the top-left circle with two secants:** Given: Outside segments 6 and 8, inner segment unknown (call it $x$).

1. **State the problem:** We have a frustum formed by removing a smaller cone from a larger cone. The larger cone has height 45 cm, the smaller cone removed has height 9 cm and bas

1. The term "scale factor" typically refers to the ratio by which a figure is enlarged or reduced in size in geometry. 2. It is the multiplier used to increase or decrease the dime

1. **Problem 1:** If arcs APB and CQD of a circle are congruent, find the ratio of AB : CD. Since arcs APB and CQD are congruent, their corresponding chords AB and CD are equal in

1. The problem asks to identify features that all squares have but some rhombuses do not. 2. A square is a special type of rhombus where all sides are equal and all angles are righ

1. The problem asks for the size of angle $a$ in the triangle formed by points $A$, $B$, and $C$ on the circle. 2. Since points $A$, $B$, and $C$ lie on a circle, the triangle $ABC

1. **State the problem:** We are given a triangle with angles 70° and 61°, and the side opposite the 61° angle is 15 units. We need to find the length of the side opposite the 70°

1. **State the problem:** Given that $\angle SUT \cong \angle YXZ$, prove that the vectors $\overrightarrow{WY}$ and $\overrightarrow{TV}$ are parallel. 2. **Analyze the given info

1. **State the problem:** Given that $\angle SUT \cong \angle YXZ$, prove that the vectors $\overrightarrow{WY}$ and $\overrightarrow{TV}$ are parallel. 2. **Analyze the given info

1. **State the problem:** We have a triangle with angles 96° and 25°, and the side opposite the 25° angle is 13 units. We need to find the side length opposite the 96° angle using

1. The problem is to prove a geometric property or theorem step by step. 2. First, clearly state the theorem or property to be proven.

1. **State the problem:** We have a circle with center O and tangent ABCD at point C.

1. **Problem Statement:** Prove the geometric relation $ (JL \times JG + HL \times HK) = (JH)^2 $ given the triangle $\triangle ABC$ with centroid $J$, median $BM$, altitude $AD$,

1. **Problem Statement:** We have an oval (ellipse) with radius $R=74$ and a square inside it with side length $S=46$. Points $a$, $b$, and $c$ are on these shapes, and we want for

1. **Problem statement:** We have a square with side length $S=46$ and an oval (ellipse) with radius $R=74$ intersecting the square vertically. Points $a$, $b$, and $c$ lie on the

1. **State the problem:** We are given two triangles, $\triangle ABC$ and $\triangle NLM$, with the conditions: - $m(\angle B) = m(\angle NLM)$

1. **State the problem:** We have a rectangle with width 10 m and height 8 m. Inside it, there is a parallelogram with base 2 m and height 8 m (matching the rectangle's height). We

1. **State the problem:** We need to find the area of the composite shape consisting of a large rectangle and a smaller attached rectangle (not a square since sides are 4 cm and 6

1. **State the problem:** We have a quadrilateral BACD with diagonals AD and BC drawn, dividing it into four triangles. Given that AB = BC = BD and BD is parallel to AC, and angles

1. **State the problem:** Find the obtuse angle between the hour and minute hands of a clock at 11:25 am. 2. **Calculate the minute hand angle:** The minute hand moves 6 degrees pe

1. **State the problem:** We need to find the perimeter of quadrilateral ADBC given that $AC=5$ cm, $BC=3$ cm, and $CB=DB$. 2. **Analyze the given information:** Since $CB=DB$, the