📐 geometry

1. **State the problem:** We are given a circle with center $O$ and triangle $ABC$ circumscribed about the circle such that $\angle A = 46^\circ$. We are asked to find the measure

1. **State the problem:** We are given a triangle with angles $\alpha = 45^\circ$, $\gamma = 73^\circ$, and side $b = 240$ cm opposite angle $\beta$. We need to find angle $\beta$

1. The problem is to find the measures of \( m \angle AEB \), \( m BC \), and \( m \angle AED \) based on the given circle with center E and arcs: AB = 90°, CD = 40°, DA = 108°, an

1. The problem asks for the distance between the points $(-3, -4)$ and $(2, 6)$. 2. We use the distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$:

1. We are asked to find the volume of a cylinder with height $h=2$ units and radius $r=3$ units. 2. The formula for the volume of a cylinder is $$V=\pi r^2 h$$ where $r$ is the rad

1. The problem states to find the volume of a cylinder with height $h=2$ units and radius $r=3$ units. 2. The formula for the volume of a cylinder is $$V = \pi r^2 h$$ where $r$ is

1. The problem is to find the volume of a cylinder with height $h=10$ units and radius $r=4$ units. 2. The formula for the volume of a cylinder is $$V=\pi r^{2}h$$ where $r$ is the

1. **Problem statement:** We have two circles with centers P (radius 6 cm) and Q (radius 5 cm), intersecting with common chord AB of length 8 cm. 2. **Find the length of PQ.**

1. The problem involves finding the angle $a$ at point $Q$ given some angles in the figure and using the variable $x$ at point $S$. 2. From the figure, angle at $P$ is given as 55°

1. The problem is to plot a series of Cartesian coordinate points and connect them with line segments sequentially to reveal a hidden animal shape. 2. The points are given as pairs

1. Бодлогыг ойлгох: ABC адил талт гурвалжин бөгөөд AC нь тойргийн диаметр, O нь төв. 2. AC диаметр гэдэг нь O цэг нь AC шугамын дунд цэг, тиймээс OA = OC.

1. The problem describes a kite-shaped quadrilateral with perpendicular diagonals. 2. The diagonals are divided into segments: one diagonal has segments 6 cm and 4 cm, so its total

1. The problem states we have a rhombus with diagonals intersecting at right angles. 2. The given diagonal lengths are 6 cm and 4 cm, but 3 cm seems ambiguous. We interpret diagona

1. **State the problem:** We have a rhombus with diagonals intersecting perpendicularly. One diagonal is divided into segments of 6 cm and 4 cm (so its total length is $6 + 4 = 10$

1. The problem is to find the area of a triangle with a base of 9 cm and a height of 5 cm. 2. The formula for the area of a triangle is given by:

1. **הגדרת הבעיה:** יש לנו משולש שווה-צלעות שכל אחת מצלעותיו באורך 9 ס"מ. 2. **מידע שניתן:** גובה המשולש הוא 5 ס"מ מנקודה על הצלע התחתונה לפסגה.

1. To find the surface area, we first need the description or formula of the surface. Please provide the equation or shape you are referring to. 2. Once the surface is defined, the

1. The problem describes an equilateral triangle with all sides equal. 2. Given two sides are 5 cm, but the base is labeled 9 cm, which contradicts the equilateral triangle propert

1. Let's identify the elements and properties of the kite from the given information. 2. The kite has two pairs of equal sides: the top pair each labeled $a$, and the other sides a

1. Stating the problem: We have points $A(-4,6)$ and $B(-1,-3)$, and we want to find point $P$ on the $x$-axis such that $P$ is equidistant from $A$ and $B$. Since $P$ lies on the

1. **State the problem:** We have a triangle ABC with a circle centered at point O inside it. Angle at vertex A is given as 46°.