📐 geometry

1. Problem: Given that RO = 2x + 6 and KC = 5x - 3 in parallelogram □ROCK, find x. Step 1: State the property used: In a parallelogram, the diagonals bisect each other, so RO = KC.

1. **State the problem:** We have an isosceles triangle ABC with AB = AC, and angles ABC and ACB given by expressions in terms of $x$: $\angle ABC = 3x^2 - 2x + 4$ degrees and $\an

1. The user asked for geometry problems with images. 2. Currently, I cannot generate or embed images directly.

1. **Stating the problem:** Find the area of circular sectors with given radii and angles.

1. The problem is to find the volume of solids with bases that are regular polygons. 2. The general formula for the volume of a prism is $$V = B \times h$$ where $B$ is the area of

1. Let's start by stating the problem: We want to find the volume of a solid whose base is a regular polygon. 2. The volume of such a solid is generally found by multiplying the ar

1. The problem asks to fill in the blanks related to triangle terminology and properties. 2. a) The line joining a vertex of a triangle to the midpoint of the opposite side is call

1. Problem Q5: In the given figure find the value of $x$. 2. Given: four points $A,B,C,D$ on a circle clockwise, chords $AB,AC,AD,CD$ are drawn, an interior point $P$ is intersecti

1. **Problem Statement:** Given a circle with center $O$, diameter $AB$, and points $C$, $D$, $E$ on the circumference such that $BC = BE$ and $\angle ADC = 120^\circ$, find the me

1. Problem Q5: Two chords AB and CD intersect inside a circle at point P with $\angle ABP=40^\circ$, $\angle BPC=110^\circ$, and $\angle CDP=x$; find $x$. 2. Formula and rules: For

1. **Problem Statement:** We are given a circle with points A, B, C, D on the circumference forming a quadrilateral. The angle at point D inside the circle is $80^\circ$. At point

1. **Problem Statement:** We are given a circle with chords AB and CD intersecting at point P inside the circle. The angle at B is 40°, the angle formed at P by chords AB and CD is

1. **Problem Statement:** We are given a circle with chords AB and CD intersecting at point P inside the circle. We know \(\angle BAP = 40^\circ\) and \(\angle APD = 110^\circ\). W

1. **Problem Statement:** We are given a figure with three intersecting lines forming two adjacent triangles. The angles given are $50^\circ$ (top horizontal angle) and $120^\circ$

1. **Problem Statement:** We are given a geometric diagram with angles $x$, $y$, $50^\circ$, and $120^\circ$. We need to find the values of $x$ and $y$ based on the given angles. 2

1. **Find the value of x in each figure:** (i) Angles on a straight line sum to 180°.

1. **Problem Statement:** Find the area of a sector of a circle with diameter 22 feet and central angle $\frac{3\pi}{4}$ radians. 2. **Formula:** The area $A$ of a sector with radi

1. **Problem Statement:** Prove that the diagonals of a rectangle are equal. 2. **Given:** Rectangle ABCD with diagonals AC and BD intersecting at point O.

1. **Problem statement:** We have a rectangle ABCD formed by two adjacent squares ABFE and CDEF, each with side length 6 cm. Point G is the midpoint of DE, and BG intersects EF at

1. 問題陳述： (1) 三個半徑為2.5 cm的圓形組成的圖形，求其周界。

1. 問題陳述： (1) 計算圖中圓的周界。