Chord AB is inclined at 70° at B to its tangent, hence it also subtends the same angle at C. Since Arc BC subtends θ at A, Arc AC subtends 3θ/2 at B. θ+3θ/2=110 θ = 44°
It's not said at the begining of the video that AB and BP are tangent lines to the circle and the drawing is misleading about it. Could be nice if you can edit it.
△PAB is an isosceles triangle (because tangents PA and PB are of the same length). Hence ∠ABP=∠BAP => ∠ABP=(180°-40°)/2=70°. By alternate segment theorem (also known as tangent-chord theorem), ∠ACB=∠ABP Hence ∠ACB=70° Thus, in triangle △ABC, ∠C=70°. Angles ∠A and ∠B must then add up to (180°-70°=1110°) It's known that the length of an arc is proportional to the angle subtended by the arc. Thus, ∠A and ∠B must be in the ratio 2:3. We've already established that ∠A+∠B=110°. Thus, to find the values of ∠A and ∠B, we divide 110° in the ratio 2:3 Hence ∠A=110°*2/(2+3)=44°
O desenho da questão não é claro inicialmente. Se A e B não são pontos de tangência a questão é difícil conclusão. Mesmo assim a questão (com pontos de tangência) é muito boa. Parabéns pela escolha. Brasil - Outubro de 2024.
Chord AB is inclined at 70° at B to its tangent, hence it also subtends the same angle at C. Since Arc BC subtends θ at A, Arc AC subtends 3θ/2 at B.
θ+3θ/2=110
θ = 44°
Nice
alternate segment theorem
you mean: θ : 2 = B : 3 ??
@@soli9mana-soli4953 Yes, they're proportional.
It's not said at the begining of the video that AB and BP are tangent lines to the circle and the drawing is misleading about it. Could be nice if you can edit it.
Yes, the tangency is not declared
The measure of the inscribed angle is proportional to the length of the arc that it encloses. From this we assume that
ازيك يا عمنا عامل ايه؟بتعمل ايه هنا.انت منين؟
Nice and simple! 👌
@@Just0Me359 أنا من الجزائر واحب قنوات الرياضيات وانت من الظاهر مصري اليس كذالك؟
△PAB is an isosceles triangle (because tangents PA and PB are of the same length). Hence ∠ABP=∠BAP => ∠ABP=(180°-40°)/2=70°.
By alternate segment theorem (also known as tangent-chord theorem), ∠ACB=∠ABP
Hence ∠ACB=70°
Thus, in triangle △ABC, ∠C=70°. Angles ∠A and ∠B must then add up to (180°-70°=1110°)
It's known that the length of an arc is proportional to the angle subtended by the arc. Thus, ∠A and ∠B must be in the ratio 2:3. We've already established that ∠A+∠B=110°. Thus, to find the values of ∠A and ∠B, we divide 110° in the ratio 2:3
Hence ∠A=110°*2/(2+3)=44°
Internal angles of circle:
α₁ = 360° - 2*90° - 40° = 140°
α₂+α₃ = 360° - α₁ = 220°
Simple rule of three:
α₂ = 2/5 (α₂+α₃) = 88°
Requested angle:
θ = ½α₂ = 44° ( Solved √ )
Extremely complicated video solution, there no need to introduce variable "x" neither "r" radius of circle
O desenho da questão não é claro inicialmente. Se A e B não são pontos de tangência a questão é difícil conclusão. Mesmo assim a questão (com pontos de tangência) é muito boa. Parabéns pela escolha. Brasil - Outubro de 2024.
done in just 2 minutes but please tell me from where you find these questions
The answer is 44°. Looks like I shall use this for practice!!!
140=2(180-θ-3/2θ)...5/2θ=110...θ=220/5=44
asnwer=55 isit
asnwer=44 isit
(2)^2(3)^2={4+9}=13 {60°A+60°B+60°C}=180°ABC/13=10.50 10.5^10 2^5.5^2^5 1^1.1^2^1 2^1(ABC ➖ 2ABC+1).