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Aug
4
comment Is it possible to find $a$, $b$ such that $(a,b] \cap \mathbb{Q} = \emptyset$?
Let $\delta = b-a$. Since $a$, $b$ are real numbers, there are sequences of rational numbers $\alpha_k>a$ and $\beta_k<b$ so that $\alpha_k\to a$ and $\beta_k \to b$ (why?). Then, for adequately large $k$, i.e., $k>k_0$, $|\alpha_k-a|<\delta/2$ and $|\beta_k-b|<\delta/2$. Then for $k>k_0, $(\alpha_k+\beta_k)/2$ is in $(a, b]$ and is a rational number.
Aug
3
awarded  Nice Question
Jul
31
revised Find the area of a triangle given the radius of its incircle and a tangential point
added 2 characters in body
Jul
31
comment Find the area of a triangle given the radius of its incircle and a tangential point
@Sawarnik That's interesting! But, could you provide a reference to the above formula for $\Delta$?
Jul
31
comment Find the area of a triangle given the radius of its incircle and a tangential point
Could you provide some references about $rR=\alpha\beta$ and $S=R(x-\alpha-\beta)$ (which means that $S=R\cdot BE$)?
Jul
31
comment Find the area of a triangle given the radius of its incircle and a tangential point
@RobArthan I have made some modifications in my answer and wrote $S$ in a simpler form which agrees with the answers of other contributors.
Jul
31
revised Find the area of a triangle given the radius of its incircle and a tangential point
added 145 characters in body
Jul
31
revised Find the area of a triangle given the radius of its incircle and a tangential point
added 16 characters in body
Jul
31
comment Find the area of a triangle given the radius of its incircle and a tangential point
@Sawarnik What are $a$ and $b$? It should be $a=s-\alpha=\beta+BE$ and $b=s-\beta=\alpha+BE$ but I can't see how this helps.
Jul
31
comment Find the area of a triangle given the radius of its incircle and a tangential point
@RobArthan Yes, there was indeed a typo in the question. Thanks for pointing this out.
Jul
31
revised Find the area of a triangle given the radius of its incircle and a tangential point
edited body
Jul
31
revised Find the area of a triangle given the radius of its incircle and a tangential point
added 68 characters in body
Jul
31
comment Find the area of a triangle given the radius of its incircle and a tangential point
@DavidQuinn The area of $ABC$ is $S=r\tau$ where $\tau$ is the semiperimeter of $ABC$, i.e., $\tau=(AB+BC+CA)/2$. I updated my answer with the complete formula of $S$.
Jul
31
asked Find the area of a triangle given the radius of its incircle and a tangential point
Jul
31
answered Find the area of a triangle given the radius of its incircle and a tangential point
May
23
revised Why a particular type of definition for increasing sequence is chosen?
Changed >= into \geq
May
23
reviewed No Action Needed Argument of complex number $(\tan \theta)$
May
23
awarded  Citizen Patrol
May
23
reviewed No Action Needed Difference between $A \equiv B \pmod {n}$ and $A \pmod {n}$
May
23
revised How to solve $12-\sin(\theta)=\cos(2\theta)$?
Typos and errors in TeX