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MATH / In the diagram below, triangle ABC is inscribed in the circle and AC=AB. The measure of angle BAC is 42 degrees and segment ED is tangent to the circle at point C. What is the meas…

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problem

In the diagram below, triangle ABCABC is inscribed in the circle and AC=ABAC = AB. The measure of angle BACBAC is 42 degrees and segment EDED is tangent to the circle at point CC. What is the measure of angle ACDACD? [asy] import olympiad; import geometry; size(150); defaultpen(linewidth(0.8)); draw(Circle((0,0),1)); draw((dir(-30).x -1,dir(-30).y-2)--(dir(-30).x+1,dir(-30).y+2)); pair C = dir(-30), B = dir(-114), A = dir(-114-138), D = (dir(-30).x+1,dir(-30).y+2), E = (dir(-30).x -1,dir(-30).y-2); draw(A--B--C--cycle); label("AA",A,N); label("BB",B,SW); label("CC",C,dir(0)); label("DD",D,dir(0)); label("EE",E,dir(-90)); [/asy]
Plain-text mathematical notation (without MathML)
In the diagram below, triangle ABC is inscribed in the circle and AC=AB. The measure of angle BAC is 42 degrees and segment ED is tangent to the circle at point C. What is the measure of angle ACD? [asy]
import olympiad; import geometry; size(150); defaultpen(linewidth(0.8));

draw(Circle((0,0),1));
draw((dir(-30).x -1,dir(-30).y-2)--(dir(-30).x+1,dir(-30).y+2));
pair C = dir(-30), B = dir(-114), A = dir(-114-138), D = (dir(-30).x+1,dir(-30).y+2), E = (dir(-30).x -1,dir(-30).y-2);
draw(A--B--C--cycle);
label("A",A,N); label("B",B,SW); label("C",C,dir(0)); label("D",D,dir(0)); label("E",E,dir(-90));
[/asy]
Original LaTeX notation
In the diagram below, triangle $ABC$ is inscribed in the circle and $AC = AB$. The measure of angle $BAC$ is 42 degrees and segment $ED$ is tangent to the circle at point $C$. What is the measure of angle $ACD$? [asy]
import olympiad; import geometry; size(150); defaultpen(linewidth(0.8));

draw(Circle((0,0),1));
draw((dir(-30).x -1,dir(-30).y-2)--(dir(-30).x+1,dir(-30).y+2));
pair C = dir(-30), B = dir(-114), A = dir(-114-138), D = (dir(-30).x+1,dir(-30).y+2), E = (dir(-30).x -1,dir(-30).y-2);
draw(A--B--C--cycle);
label("$A$",A,N); label("$B$",B,SW); label("$C$",C,dir(0)); label("$D$",D,dir(0)); label("$E$",E,dir(-90));
[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
6a922710-27d4-5fbe-ac85-67e6c12b6501
task_key
geometry--test--6a922710-27d4-5fbe-ac85-67e6c12b6501
task_revision_id
1
config / split
geometry / test

Official source

initial import