📐 geometry

1. Problem: Find the circumference of circles with given radii or diameters using $\pi = \frac{22}{7}$. (a) Radius $r=8$ cm. Circumference formula: $$C=2\pi r$$

1. The problem states that we have a right-angled triangle with two equal-length sides. 2. In a right-angled triangle, one angle is always $90^\circ$.

1. **State the problem:** We need to find the distance from point A to point G in a right prism with given dimensions. 2. **Understand the prism structure:** The base EFGH is a rec

1. **Problem 9:** Given points C and D on a circle with diameter AB, and BC = AC = 4 cm. (a) Find length AD that maximizes the area of quadrilateral ACBD.

1. समस्या: एक बेलनाकार पात्र जिसकी त्रिज्या $3.5$ मीटर है, पानी से भरा हुआ है। इसमें से $15400$ लीटर पानी निकाला जाता है। हमें पानी के स्तर में गिरावट ज्ञात करनी है। 2. पहले, लीटर

1. في السؤال الأول، نلاحظ أن الزاوية عند النقطة 4 هي 125°، وهي أكبر من الزوايا الأخرى المعطاة (30° عند النقطة 2). 2. في السؤال الثاني، لدينا مثلثان متطابقان △ABD ≅ △CDB.

1. **Problem statement:** (a) Enlarge triangle A with scale factor $\frac{1}{3}$ and centre of enlargement $(2,6)$.

1. **State the problem:** We have a circle with a triangle inscribed. One angle inside the circle is $37^\circ$. There is a tangent line touching the circle at the vertex where the

1. **Problem 11:** In triangles ΔRST and ΔUVW, given RT = 6x - 2, UW = 2x + 7, and angles ∠R = ∠U, ∠S = ∠V, find $x$ so that ΔRST ≅ ΔUVW. 2. Since two angles are equal, by the Angl

1. **State the problem:** We are given the quadrilaterals ARST and AUVW with the following side lengths: - RT = 6x - 2

1. **Problem:** Construct triangle ABC with $AB=5$ cm, $\angle ABC=75^\circ$, and circumradius $R=3.5$ cm using ruler and compass. Step 1: Draw segment $AB=5$ cm.

1. Problem: Construct triangle ABC with AB = 5 cm, angle ABC = 75°, and circumradius = 3.5 cm using ruler and compass. Step 1: Draw segment AB = 5 cm.

1. **State the problem:** We have an isosceles triangle with an exterior angle of 128° adjacent to one vertex, and we need to find the interior angle $z$ opposite this exterior ang

1. **State the problem:** We need to find all values of $x$ such that the triangle with vertices $A(3,3,x)$, $B(0,3,-7)$, and $C(2,5,-9)$ has an area of 4. 2. **Recall the formula

1. **State the problem:** We need to find all values of $x$ such that the triangle with vertices $A(x,4,-1)$, $B(0,4,-3)$, and $C(2,1,1)$ has a right angle at vertex $A$. 2. **Reca

1. The problem states that point K is the image of point J under a translation vector \(\begin{pmatrix} m \\ n \end{pmatrix}\), and the distance between J and K is 13 units. 2. Giv

1. The problem states that the area of quadrilateral ADEF is 6 cm² and asks for the area of quadrilateral AD'E'F'. 2. To find the area of AD'E'F', we need to understand the relatio

1. The term "arc" in mathematics typically refers to a portion of the circumference of a circle. 2. More specifically, an arc is a continuous part of the circle's edge between two

1. The problem involves a cyclic quadrilateral WXYZ inscribed in a circle, with angles at vertices W and X given as 44° and 24° respectively. 2. In a cyclic quadrilateral, opposite

1. **State the problem:** We have a large triangle with angles labeled $n$ at the bottom-left vertex, $3n$ at the top vertex, and the base angle split into two adjacent angles $2m$

1. The problem asks to identify the name, number of vertices, sides, and angles for triangles labeled with points P, Q, and R. 2. A triangle is a polygon with 3 vertices, 3 sides,