📐 geometry

1. সমস্যাটি হলো: একটি বৃত্তে ABC ত্রিভুজের কোণ $\angle ABC = 30^\circ$ এবং বৃত্তের ব্যাসার্ধ $5$ মিটার। আমাদের অর্ধবৃত্তের ব্যাসার্ধ নির্ণয় করতে হবে। 2. সূত্র: বৃত্তের ব্যাসার্ধ $

1. **সমস্যা:** একটি সমবাহু ত্রিভুজের প্রতি এক বাহুর দৈর্ঘ 4 মিটার বাড়ালে ক্ষেত্রফল 20\sqrt{3} বর্গমিটার হয়। ত্রিভুজটির মূল বাহুর দৈর্ঘ্য নির্ণয় কর। 2. **সূত্র:** সমবাহু ত্রিভুজে

1. 問題陳述：計算一個圓形噴水池的面積，已知圓周長為 37.68 m，取 π = 3.14。 2. 公式與規則：

1. **Nêu bài toán:** Cho tam giác nhọn ABC với các đường cao AD, BE, CF. Gọi K, L lần lượt là tâm đường tròn nội tiếp các tam giác CDE, BDF. Gọi P, Q lần lượt là tâm đường tròn ngo

1. **Problem Statement:** Find the values of angles $a$, $b$, $c$, and $d$ in the circle with center $O$ where $PQ$ is tangent at $A$. Given angles: $\angle C = 110^\circ$, $\angle

1. **Problem 5:** Given a circle with center O, tangent PQ at A, and angles marked as $110^\circ$ at C, $60^\circ$ at D, and unknown angles $a$, $b$, $c$, and $d$. Find $a$, $b$, $

1. **Problem statement:** We have an isosceles triangle with two equal sides of length 8 cm and an included angle of 55° between them. We need to find the angle $x$ at the top vert

1. **State the problem:** We have an isosceles triangle PQR symmetrical about axis m, with angle Q measuring 35°. We need to find the measure of angle XPR.

1. **State the problem:** We need to find the perimeter of a right triangle with a height of 9 cm perpendicular to the base, which is divided into two segments of 4 cm and 12 cm. 2

1. **State the problem:** We are given a right-angled triangle with two shorter sides (legs) measuring 14 cm and 26 cm. We need to find the length of the hypotenuse. 2. **Formula u

1. **State the problem:** We have three similar solid cylinders L, M, and P made from the same material. Given masses and surface areas, we need to find the ratio of their heights:

1. The problem asks for the order of rotational symmetry of a shape that looks like a three-pointed star or propeller. 2. Rotational symmetry order is the number of times a shape f

1. **Problem statement:** We have a circle with center $O$ and points $A$, $B$, $C$, and $D$ on the circumference. $FDE$ is a tangent line touching the circle at $D$. We are given

1. **Problem statement:** We need to find the area of the shaded segment of a circle. The sector has radius $r=16$ cm and central angle $\theta=140.3^\circ$. The chord length is 30

1. **Problem statement:** Find the coordinates of point P which is 5 cm from BC and 4 cm from A's altitude in rectangle ABCD with AB = 8 cm and BC = 6 cm. 2. **Formula and rules:**

1. **Problem:** Given a circle with center O, angles \(\angle OAB = 30^\circ\) and \(\angle OCB = 40^\circ\), find \(\angle AOC\). 2. **Formula and rules:** In a circle, the angle

1. The problem asks to find the result of translating point R(-5,8) by the translation vector T = [-3,-4]. 2. The formula for translation is:

1. **Stating the problem:** We have a right triangle RST with a right angle at vertex S.

1. **State the problem:** We need to prove that the tangent line ABC at point B is parallel to the chord EF of the circle. 2. **Given:**

1. **State the problem:** We need to prove that the tangent line ABC at point B is parallel to the chord EF of the circle. 2. **Given:**

1. **State the problem:** We are given points A(2, -2), B(2, 3), C(-1, 5), and D(-1, 0) which form a parallelogram ABCD. We need to find the perimeter of this parallelogram. 2. **R