📐 geometry

1. ප්‍රශ්නය: 28 cm පසැලැස්සූ චතුරස්‍රයක (ABCD) A කේන්ද්‍රයෙන් බිත්තියක් ලෙස quarter circle එකක් ඇඳී ඇත. අපිට එහි විවිධ ගණිතමය ගුණාංග සොයාගත යුතුය. 2. පළමුව, quarter circle එකේ ආරම්

1. **State the problem:** Find the midpoint of the points $A(15, 18)$ and $B(15, 18)$. 2. **Formula:** The midpoint $M$ of two points $A(x_1, y_1)$ and $B(x_2, y_2)$ is given by:

1. Let's start by defining the problem: We need to determine whether a given scalene triangle is obtuse or acute. 2. Recall the definitions:

1. **Problem:** Determine the type of triangle based on the lengths of the sides. 2. **Formula and rules:**

1. The problem is to graph the coordinates, but no specific coordinates were provided. 2. To graph coordinates, you need pairs of numbers in the form $(x, y)$.

1. **State the problem:** We need to find the area of quadrilateral ACDE given the sides and angles: AB = 10 cm, AE = 21 cm, BC = 20 cm, and angle CDE = 150°. 2. **Analyze the figu

1. **Problem statement:** We have a rhombus ABCD with side length 7 cm, angle \(\angle D = 120^\circ\), and \(\angle C = 60^\circ\). We need to find the length of diagonal AC to 1

1. **Problem statement:** We have a rhombus ABCD with side length 9 cm, angles \(\angle D = 100^\circ\) and \(\angle C = 80^\circ\). We need to find the length of diagonal AC to 1

1. **State the problem:** We are given an L-shaped polygon with dimensions involving $x$ and the total area is 137 cm². We need to show that the equation $3x^2 + 2x - 120 = 0$ hold

1. **Problem Statement:** Given two planes with equations $\vec{r} \cdot \hat{a} = p$ and $\vec{r} \cdot \vec{b} - q = 0$, find:

1. **Problem statement:** Given a circle with center $O$, points $A$, $B$, and $C$ lie on the circumference. $AB$ is a side of a regular pentagon (5-sided polygon) inscribed in the

1. **Problem Statement:** Given a circle with center $O$, points $A$, $B$, and $C$ lie on the circumference. $AB$ is a side of a regular pentagon (5-sided polygon) inscribed in the

1. The problem asks to create two squares each with side length 10 cm, divided into 100 equal smaller squares. 2. Each small square will have side length $\frac{10}{10} = 1$ cm bec

1. **Stating the problem:** We have a quadrilateral ABDM with diagonal AC. Angles at vertices are labeled as follows: angles $p$ and $w$ at vertex A, angle $t$ at vertex B, and ang

1. **Stating the problem:** Triangles $XYZ$ and $PQR$ are similar. Given sides $XY=35$, $YZ=30$, $XZ=X$, and corresponding sides $PQ=28$, $QR=12$, $PR=n$, find $X$ and $n$. 2. **Fo

1. The problem asks to find the values of $x$, $y$, and $z$ given some angles: $40^\circ$, $121^\circ$, and others labeled $A$, $B$, $C$, $D$, $z^\circ$, $x^\circ$, $y^\circ$. 2. S

1. **Stating the problem:** We need to find the values of angles $x$, $y$, and $z$ given some angles and possibly relationships between them. 2. **Analyzing the given information:*

1. **State the problem:** Find the length of the longest segment that can fit into a cube with side length 4 cm. 2. **Formula used:** The longest segment inside a cube is its space

1. **State the problem:** We have a quadrilateral ABCD with diagonals intersecting inside, and various angles given including two angles labeled $x$ at vertices A and D. We need to

1. **State the problem:** In rectangle ABCD, we are given that DE = 3x + 6 and BE = 5x - 6. We need to find the value of $x$. 2. **Understand the properties of a rectangle:** In a

1. **State the problem:** We are given a quadrilateral ABCD with interior angles \(\angle A = 50^\circ\), \(\angle B = 60^\circ\), \(\angle C = 10^\circ\), and \(\angle D = 70^\cir