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MATH / In acute triangle ABC, ∠A=68^(∘). Let O be the circumcenter of triangle ABC. Find ∠OBC, in degrees. [asy] unitsize(1 cm); pair A, B, C, O; A = (1,2); B = (0,0); C = (3,0); O = circ…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

In acute triangle ABCABC, ∠A=68∘\angle A = 68^\circ. Let OO be the circumcenter of triangle ABCABC. Find ∠OBC\angle OBC, in degrees. [asy] unitsize(1 cm); pair A, B, C, O; A = (1,2); B = (0,0); C = (3,0); O = circumcenter(A,B,C); draw(A--B--C--cycle); draw(circumcircle(A,B,C)); draw(B--O); label("AA", A, N); label("BB", B, SW); label("CC", C, SE); dot("OO", O, NE); [/asy]
Plain-text mathematical notation (without MathML)
In acute triangle ABC, ∠A=68^(∘).  Let O be the circumcenter of triangle ABC.  Find ∠OBC, in degrees.

[asy]
unitsize(1 cm);

pair A, B, C, O;

A = (1,2);
B = (0,0);
C = (3,0);
O = circumcenter(A,B,C);

draw(A--B--C--cycle);
draw(circumcircle(A,B,C));
draw(B--O);

label("A", A, N);
label("B", B, SW);
label("C", C, SE);
dot("O", O, NE);
[/asy]
Original LaTeX notation
In acute triangle $ABC$, $\angle A = 68^\circ$.  Let $O$ be the circumcenter of triangle $ABC$.  Find $\angle OBC$, in degrees.

[asy]
unitsize(1 cm);

pair A, B, C, O;

A = (1,2);
B = (0,0);
C = (3,0);
O = circumcenter(A,B,C);

draw(A--B--C--cycle);
draw(circumcircle(A,B,C));
draw(B--O);

label("$A$", A, N);
label("$B$", B, SW);
label("$C$", C, SE);
dot("$O$", O, NE);
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
9090e8fd-c0b1-5bd4-87e1-c19f8c496d30
task_key
geometry--test--9090e8fd-c0b1-5bd4-87e1-c19f8c496d30
task_revision_id
1
config / split
geometry / test

Official source

initial import