How to calculate the distance of the circumcenter to one of the sides of a triangle inscribed in a circle?

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In a triangle $ ABC $, the $ ∠A = 53 ° $ and the circumference measures $ 20 $, calculates the double of the distance to the $overlineBCquad$side.



I do not understand the question why it asks for the distance of the circumcision to the $overlineBCquad$side, and this distance varies according to the point on the $overlineBCquad$side of the triangle. On the other hand, if it would be the distance from the cicuncentro to one of the points between $B$ and $C$ of the circumference, it would be $40$ ... But the answer is $24$.



Circunference




geometry trigonometry euclidean-geometry circle




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  • Did you mean the radius is 20?
    – David K
    Jul 30 at 17:51














up vote
-1
down vote

favorite












In a triangle $ ABC $, the $ ∠A = 53 ° $ and the circumference measures $ 20 $, calculates the double of the distance to the $overlineBCquad$side.



I do not understand the question why it asks for the distance of the circumcision to the $overlineBCquad$side, and this distance varies according to the point on the $overlineBCquad$side of the triangle. On the other hand, if it would be the distance from the cicuncentro to one of the points between $B$ and $C$ of the circumference, it would be $40$ ... But the answer is $24$.



Circunference




geometry trigonometry euclidean-geometry circle




share|cite|improve this question





















  • Did you mean the radius is 20?
    – David K
    Jul 30 at 17:51












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











In a triangle $ ABC $, the $ ∠A = 53 ° $ and the circumference measures $ 20 $, calculates the double of the distance to the $overlineBCquad$side.



I do not understand the question why it asks for the distance of the circumcision to the $overlineBCquad$side, and this distance varies according to the point on the $overlineBCquad$side of the triangle. On the other hand, if it would be the distance from the cicuncentro to one of the points between $B$ and $C$ of the circumference, it would be $40$ ... But the answer is $24$.



Circunference




geometry trigonometry euclidean-geometry circle




share|cite|improve this question













In a triangle $ ABC $, the $ ∠A = 53 ° $ and the circumference measures $ 20 $, calculates the double of the distance to the $overlineBCquad$side.



I do not understand the question why it asks for the distance of the circumcision to the $overlineBCquad$side, and this distance varies according to the point on the $overlineBCquad$side of the triangle. On the other hand, if it would be the distance from the cicuncentro to one of the points between $B$ and $C$ of the circumference, it would be $40$ ... But the answer is $24$.



Circunference





geometry trigonometry euclidean-geometry circle





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 30 at 17:27









Michael Rozenberg

87.7k1578179




87.7k1578179









asked Jul 30 at 15:48









Payo

61




61











  • Did you mean the radius is 20?
    – David K
    Jul 30 at 17:51
















  • Did you mean the radius is 20?
    – David K
    Jul 30 at 17:51















Did you mean the radius is 20?
– David K
Jul 30 at 17:51




Did you mean the radius is 20?
– David K
Jul 30 at 17:51










1 Answer
1






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0
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Let $O$ be a center of the circle and $OD$ be a perpendicular from $O$ to $BC$.



I think it means to find $2OD$.



Since $$measuredangle COD=frac12measuredangle BOC=53^circ,$$
we obtain:
$$2OD=2cdot20cos53^circ=24.07...$$






share|cite|improve this answer





















  • Excuse me it was my mistake, they asked me twice the distance of the circumcenter to the $overlineBCquad$ side.
    – Payo
    Jul 30 at 16:25










  • @Payo It's exactly, which I got.
    – Michael Rozenberg
    Jul 30 at 16:26











  • @Michael- My mistake
    – Love Invariants
    Jul 30 at 16:30










  • Yes, Thank you @Michael
    – Payo
    Jul 30 at 16:40










  • You are welcome!
    – Michael Rozenberg
    Jul 30 at 17:26










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
0
down vote













Let $O$ be a center of the circle and $OD$ be a perpendicular from $O$ to $BC$.



I think it means to find $2OD$.



Since $$measuredangle COD=frac12measuredangle BOC=53^circ,$$
we obtain:
$$2OD=2cdot20cos53^circ=24.07...$$






share|cite|improve this answer





















  • Excuse me it was my mistake, they asked me twice the distance of the circumcenter to the $overlineBCquad$ side.
    – Payo
    Jul 30 at 16:25










  • @Payo It's exactly, which I got.
    – Michael Rozenberg
    Jul 30 at 16:26











  • @Michael- My mistake
    – Love Invariants
    Jul 30 at 16:30










  • Yes, Thank you @Michael
    – Payo
    Jul 30 at 16:40










  • You are welcome!
    – Michael Rozenberg
    Jul 30 at 17:26














up vote
0
down vote













Let $O$ be a center of the circle and $OD$ be a perpendicular from $O$ to $BC$.



I think it means to find $2OD$.



Since $$measuredangle COD=frac12measuredangle BOC=53^circ,$$
we obtain:
$$2OD=2cdot20cos53^circ=24.07...$$






share|cite|improve this answer





















  • Excuse me it was my mistake, they asked me twice the distance of the circumcenter to the $overlineBCquad$ side.
    – Payo
    Jul 30 at 16:25










  • @Payo It's exactly, which I got.
    – Michael Rozenberg
    Jul 30 at 16:26











  • @Michael- My mistake
    – Love Invariants
    Jul 30 at 16:30










  • Yes, Thank you @Michael
    – Payo
    Jul 30 at 16:40










  • You are welcome!
    – Michael Rozenberg
    Jul 30 at 17:26












up vote
0
down vote










up vote
0
down vote









Let $O$ be a center of the circle and $OD$ be a perpendicular from $O$ to $BC$.



I think it means to find $2OD$.



Since $$measuredangle COD=frac12measuredangle BOC=53^circ,$$
we obtain:
$$2OD=2cdot20cos53^circ=24.07...$$






share|cite|improve this answer













Let $O$ be a center of the circle and $OD$ be a perpendicular from $O$ to $BC$.



I think it means to find $2OD$.



Since $$measuredangle COD=frac12measuredangle BOC=53^circ,$$
we obtain:
$$2OD=2cdot20cos53^circ=24.07...$$







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Jul 30 at 16:16









Michael Rozenberg

87.7k1578179




87.7k1578179











  • Excuse me it was my mistake, they asked me twice the distance of the circumcenter to the $overlineBCquad$ side.
    – Payo
    Jul 30 at 16:25










  • @Payo It's exactly, which I got.
    – Michael Rozenberg
    Jul 30 at 16:26











  • @Michael- My mistake
    – Love Invariants
    Jul 30 at 16:30










  • Yes, Thank you @Michael
    – Payo
    Jul 30 at 16:40










  • You are welcome!
    – Michael Rozenberg
    Jul 30 at 17:26
















  • Excuse me it was my mistake, they asked me twice the distance of the circumcenter to the $overlineBCquad$ side.
    – Payo
    Jul 30 at 16:25










  • @Payo It's exactly, which I got.
    – Michael Rozenberg
    Jul 30 at 16:26











  • @Michael- My mistake
    – Love Invariants
    Jul 30 at 16:30










  • Yes, Thank you @Michael
    – Payo
    Jul 30 at 16:40










  • You are welcome!
    – Michael Rozenberg
    Jul 30 at 17:26















Excuse me it was my mistake, they asked me twice the distance of the circumcenter to the $overlineBCquad$ side.
– Payo
Jul 30 at 16:25




Excuse me it was my mistake, they asked me twice the distance of the circumcenter to the $overlineBCquad$ side.
– Payo
Jul 30 at 16:25












@Payo It's exactly, which I got.
– Michael Rozenberg
Jul 30 at 16:26





@Payo It's exactly, which I got.
– Michael Rozenberg
Jul 30 at 16:26













@Michael- My mistake
– Love Invariants
Jul 30 at 16:30




@Michael- My mistake
– Love Invariants
Jul 30 at 16:30












Yes, Thank you @Michael
– Payo
Jul 30 at 16:40




Yes, Thank you @Michael
– Payo
Jul 30 at 16:40












You are welcome!
– Michael Rozenberg
Jul 30 at 17:26




You are welcome!
– Michael Rozenberg
Jul 30 at 17:26












 

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