📐 geometry

1. The problem states that in a geometric figure with points C, D, A, B, and E, we know the lengths $DA = 13.7$, $EB = 17.1$, and $CD = 18.3$. We are asked to find the length $CE$.

1. Diketahui segitiga ABC siku-siku di B dengan sisi $a = AB$, $b = BC$, dan $c = AC$ sebagai hipotenusa. 2. Titik D terletak pada sisi AC sehingga sudut $ADB$ adalah 90°, artinya

1. The problem asks for the equation of a circle given its center and a point on its circumference. 2. Recall that the equation of a circle with center $(h,k)$ and radius $r$ is:

1. **Problem Statement**: Given line segment $PQ=7$ cm, construct triangle $PQR$ so that $QR=6$ cm and $\angle RPQ=60^\circ$. Then construct the perpendicular to $PR$ passing throu

1. **Problem Statement:** We are given that in triangle ABC, the sides and angles satisfy the relation $$a^2 (1 + \cos A) = 2bc \sin^2 A$$, and we need to determine the shape of th

1. The problem is to analyze the given equation of a circle: $$(x + 3)^2 + (y + 5)^2 = 25$$ 2. This equation is in the standard form of a circle: $$(x - h)^2 + (y - k)^2 = r^2$$ wh

1. The problem states: "Total surface area of a cube is 1350 sq. m. Find its volume." 2. Recall that the total surface area $A$ of a cube with side length $s$ is given by the formu

1. Stating the problem: We have the equation of a circle $$(x + 3)^2 + (y + 5)^2 = 25$$ 2. Find the center and radius:

1. Problem: Find length AP in the first triangle where AP is a median, BC = 18, and $AB^2 + AC^2 = 260$. 2. P is midpoint of BC, so $BP = \frac{1}{2} BC = \frac{1}{2} \times 18 = 9

1. Тэгш өнцөгт гурвалжин гурав дахь өнцөг нь $30^\circ$ байх үед, түүний бусад хоёр өнцөгийг олох. Тэгш өнцөгт гурвалжны ямар ч хоёр өнцөг хамтад $90^\circ$ байхаас, үлдэгдэл өнцөг

1. **230: Тэгш өнцөгт гурвалжны нэг өнцөг 30°-тай тэнцүү бол нөгөө хоёр өнцөг болон хэлеё**. Тэгш өнцөгт гурвалжны нэг өнцөг $90^\circ$ байдаг.

1. For problem 17: The slope of the wedge is given as $x$, and we need to find $\tan x$. Since slope is defined as the ratio of the vertical change to the horizontal change, $\tan

1. **State the problem:** We are given a circle with center P and diameter AB. Point C lies on the circle such that the angle formed by lines PC and PB is 41°.

1. **State the problem:** We need to find the measure of the minor arc $\overset{\frown}{BC}$ in a circle with center $P$. The segments $\overline{AC}$ and $\overline{BD}$ are diam

1. The distance between points $(-4,4)$ and $(0,-2)$ is calculated using the distance formula: $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} = \sqrt{(0-(-4))^2 + (-2-4)^2} = \sqrt{4^2 + (-6)^

1. **Problem statement:** Given a circle with diameter $\overline{AB}$, find the sizes of the angles: a) $\angle ABP$

1. Let's state the problem: We want to find the volume of a triangular prism. 2. The volume $V$ of a prism is given by the formula:

1. **State the problem:** We need to find the length of segment $PH$ where $P$ is a vertex of the rectangular base PQRS and $H$ is the midpoint of the top edge $FG$ of the wedge. G

1. **Problem statement:** We have a circle with an inscribed angle measuring 26°. A tangent touches the circle at the endpoint of the chord forming an angle $x$° with the chord out

1. The problem states that the sum of two angles $x$ and $y$ is given by $x + y = \frac{320}{3}^\circ \approx 106.67^\circ$.\n\n2. We are to understand or analyze the relationship

1. The problem is to find the volume of a cone. 2. The formula for the volume of a cone is given by