There are circle with radius R1 and circle with radius R2. We also know the distance between A and O and that angle $AOB=\varphi $. The aim is to calculate distance between B and C.

abelynybco
2022-09-27
Answered

There are circle with radius R1 and circle with radius R2. We also know the distance between A and O and that angle $AOB=\varphi $. The aim is to calculate distance between B and C.

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Libby Weaver

Answered 2022-09-28
Author has **5** answers

Step 1

From that, with the given, $\mathrm{\angle}A$ can then be found by sine theorem.

Step 2

In $\mathrm{\u25b3}AOC$, since AO, OC and $\mathrm{\angle}A$ are known, apply cosine theorem again to find AC. Result then follows.

From that, with the given, $\mathrm{\angle}A$ can then be found by sine theorem.

Step 2

In $\mathrm{\u25b3}AOC$, since AO, OC and $\mathrm{\angle}A$ are known, apply cosine theorem again to find AC. Result then follows.

asked 2022-08-22

How to prove the directed angle cyclic quadrilateral theorem?

"Prove that 4 points A,B,X,Y, no 3 collinear, are concyclic if and only if $\measuredangle XAY=\measuredangle XBY$

(Where $\measuredangle $ stands for directed angle $\phantom{\rule{0.667em}{0ex}}\mathrm{mod}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{180}^{\circ}$)"

How does a proof look like that this actually matches the "normal" cyclic quadrilateral theorem?

"Prove that 4 points A,B,X,Y, no 3 collinear, are concyclic if and only if $\measuredangle XAY=\measuredangle XBY$

(Where $\measuredangle $ stands for directed angle $\phantom{\rule{0.667em}{0ex}}\mathrm{mod}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{180}^{\circ}$)"

How does a proof look like that this actually matches the "normal" cyclic quadrilateral theorem?

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Given: Circle O

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BC is a diameter.

Prove: $m\mathrm{\angle}ACB=\frac{1}{2}mAB$

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The bisector of exterior angle of B intersects the bisector CF (F on AB) at Y. Determine the comparison of $YF:YC$ by considering a,b,c as the lengths of side of the triangle ABC.

What theorems should I use here? Or what theorems should I apply first?

What theorems should I use here? Or what theorems should I apply first?