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MATH / In the figure, point O is the center of the circle, the measure of angle RTB is 28 degrees, and the measure of angle ROB is three times the measure of angle SOT. What is the measur…

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problem

In the figure, point OO is the center of the circle, the measure of angle RTBRTB is 28 degrees, and the measure of angle ROBROB is three times the measure of angle SOTSOT. What is the measure of minor arc RSRS, in degrees? [asy] unitsize(1.2cm); defaultpen(linewidth(.7pt)+fontsize(8pt)); dotfactor=3; pair A=(0,0), B=(-1,0), T=(2,0); pair T0=T+10*dir(162); pair[] RS=intersectionpoints(Circle(A,1),T--T0); pair Sp=RS[0]; pair R=RS[1]; pair[] dots={A,B,T,Sp,R}; dot(dots); draw(Circle(A,1)); draw(B--T--R); label("TT",T,S); label("OO",A,S); label("BB",B,W); label("RR",R,NW); label("SS",Sp,NE); [/asy]
Plain-text mathematical notation (without MathML)
In the figure, point O is the center of the circle, the measure of angle RTB is 28 degrees, and the measure of angle ROB is three times the measure of angle SOT. What is the measure of minor arc RS, in degrees? [asy]
unitsize(1.2cm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
dotfactor=3;

pair A=(0,0), B=(-1,0), T=(2,0);
pair T0=T+10*dir(162);
pair[] RS=intersectionpoints(Circle(A,1),T--T0);
pair Sp=RS[0];
pair R=RS[1];
pair[] dots={A,B,T,Sp,R};
dot(dots);

draw(Circle(A,1));
draw(B--T--R);

label("T",T,S);
label("O",A,S);
label("B",B,W);
label("R",R,NW);
label("S",Sp,NE);
[/asy]
Original LaTeX notation
In the figure, point $O$ is the center of the circle, the measure of angle $RTB$ is 28 degrees, and the measure of angle $ROB$ is three times the measure of angle $SOT$. What is the measure of minor arc $RS$, in degrees? [asy]
unitsize(1.2cm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
dotfactor=3;

pair A=(0,0), B=(-1,0), T=(2,0);
pair T0=T+10*dir(162);
pair[] RS=intersectionpoints(Circle(A,1),T--T0);
pair Sp=RS[0];
pair R=RS[1];
pair[] dots={A,B,T,Sp,R};
dot(dots);

draw(Circle(A,1));
draw(B--T--R);

label("$T$",T,S);
label("$O$",A,S);
label("$B$",B,W);
label("$R$",R,NW);
label("$S$",Sp,NE);
[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
5a508b6b-5b7b-5473-92b7-3bac1cda5dea
task_key
geometry--test--5a508b6b-5b7b-5473-92b7-3bac1cda5dea
task_revision_id
1
config / split
geometry / test

Official source

initial import