📐 geometry

1. **نبدأ بملاحظة المعطيات:** لدينا نقطة $P(-1,0,1)$ ومستقيم معطى بالنسبة للمعادلات: $$\frac{1 - y}{2} = \frac{1 - y}{1} = \frac{6 + 1}{1 - z}$$

**Problem 39:** Show that the triangle with vertices A(0, 2), B(-3, -1), and C(-4, 3) is isosceles. 1. Calculate the lengths of the sides AB, BC, and CA using the distance formula:

1. **Problem Statement:** (i) Show that points A(0, 2), B(\sqrt{3}, -1), and C(0, -2) form a right-angled triangle.

1. **Problem (i):** Show that A(0,2), B(\(\sqrt{3}\),-1), C(0,-2) form a right-angled triangle. 2. Calculate lengths of sides using distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^

1. প্রশ্ন বোঝা: একটি ধাতব গোলকের ব্যাসের ক্ষেত্রফল $A$ থেকে নতুন গোলকের ব্যাসের ক্ষেত্রফল $\frac{A}{2}$ হয়েছে। এর অর্থ, নতুন গোলকের ব্যাসের ক্ষেত্রফল আগের গোলকের ক্ষেত্রফলের অর্ধেক

1. Given a right triangle ABC with \(\angle B = 90^\circ\), \(\angle C = 60^\circ\), and hypotenuse \(AC = 10\) cm. a) Find \(\angle A\).

1. Stating Question 2: A compound curve has a common tangent length of 81.6 m, making angles $15^\circ$ and $17^\circ$ with the tangents of the first and second curves respectively

1. **State the problem:** We need to find the arc measure of the major arc \(\widehat{AEB}\) in a circle with diameters \(\overline{AD}\) and \(\overline{CE}\) intersecting at the

1. The problem states that \(\overline{AD}\) and \(\overline{CE}\) are diameters of circle \(P\). 2. Since \(AD\) and \(CE\) are diameters, \(A\), \(D\), \(C\), and \(E\) lie on th

1. **State the problem:** We need to find the arc measure of the major arc BÂD on circle P, given the central angles \(\angle APB = 136^\circ\), \(\angle BPC = 74^\circ\), and \(\a

A. Find the Measure of the Central Angle 1. Problem: Given the intercepted arc measures 72° in a circle, find the measure of the central angle.

1. The problem asks us to complete statements to prove triangle ABC is congruent to triangle ADC in rectangle ABCD with diagonal AC. 2. Since ABCD is a rectangle, angles ADC and AB

1. **State the problem:** We have an isosceles triangle ABC with vertices A(-9, 11), B(-9, 0), and C(p, q). AB is parallel to the y-axis, BC is parallel to the x-axis, and the area

1. **Problem Statement:** We have rectangle ABCD where AD = 34 cm. The rectangle is folded along line AP, bringing point B to side CD at point B'. We know \(\angle AB'D = 66^\circ\

1. **State the problem:** We have rectangle ABDE and parallelogram BCDF. We need to find the perpendicular distance from point B to line DF. 2. **Identify given measurements:**

1. Xác định biểu thức vector trong câu b): Biểu diễn vectơ \(\overline{AM} = (1-k) \overline{AB} + k \overline{AC} \)

1. Cho hình bình hành ABCD tâm O, M, N lần lượt là trung điểm AB, CD. - a) Ta có \(\overrightarrow{DA} + \overrightarrow{DB} = 2 \overrightarrow{DM}\) chứng minh sử dụng trung điểm

1. The problem states a triangle \(\triangle ABC\) with sides \(AB=5\), \(AC=6\), and \(\sin \angle BAC=0.1\). We need to find its area. 2. Recall the formula for the area of a tri

1. Problem 9 states: Circles P and Q are tangent at S. AB is tangent to both circles at S. Given AB = 16, AP = 12, AQ = 10, find length PQ if it bisects AB. 2. Since AB is tangent

1. **Stating the problem:** We have an equilateral triangle $ABC$ and points $M, N, P$ defined by $BM = kBC$, $CN = \frac{2}{3}CA$, and $AP = \frac{4}{15}AB$. We examine the claim

1. **State the problem:** We are given two ellipses (Figure 1 and Figure 2) centered at the origin (0,0). 2. **Figure 1 details:**