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MATH / Distinct points A and B are on a semicircle with diameter MN and center C. The point P is on CN and ∠CAP=∠CBP=10^(∘). If arc MA is equal to 40^(∘), then find arc BN (in degrees). […

Problem

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

problem

Distinct points AA and BB are on a semicircle with diameter MNMN and center CC. The point PP is on CNCN and ∠CAP=∠CBP=10∘\angle CAP = \angle CBP = 10^\circ. If arc MAMA is equal to 40∘40^\circ, then find arc BNBN (in degrees). [asy] import geometry; import graph; unitsize(2 cm); pair A, B, C, M, N, P; M = (-1,0); N = (1,0); C = (0,0); A = dir(140); B = dir(20); P = extension(A, A + rotate(10)*(C - A), B, B + rotate(10)*(C - B)); draw(M--N); draw(arc(C,1,0,180)); draw(A--C--B); draw(A--P--B); label("AA", A, NW); label("BB", B, NE); label("CC", C, S); label("MM", M, SW); label("NN", N, SE); label("PP", P, S); [/asy]
Plain-text mathematical notation (without MathML)
Distinct points A and B are on a semicircle with diameter MN and center C.  The point P is on CN and ∠CAP=∠CBP=10^(∘).  If arc MA is equal to 40^(∘), then find arc BN (in degrees).

[asy]
import geometry;
import graph;

unitsize(2 cm);

pair A, B, C, M, N, P;

M = (-1,0);
N = (1,0);
C = (0,0);
A = dir(140);
B = dir(20);
P = extension(A, A + rotate(10)*(C - A), B, B + rotate(10)*(C - B));

draw(M--N);
draw(arc(C,1,0,180));
draw(A--C--B);
draw(A--P--B);

label("A", A, NW);
label("B", B, NE);
label("C", C, S);
label("M", M, SW);
label("N", N, SE);
label("P", P, S);
[/asy]
Original LaTeX notation
Distinct points $A$ and $B$ are on a semicircle with diameter $MN$ and center $C$.  The point $P$ is on $CN$ and $\angle CAP = \angle CBP = 10^\circ$.  If arc $MA$ is equal to $40^\circ$, then find arc $BN$ (in degrees).

[asy]
import geometry;
import graph;

unitsize(2 cm);

pair A, B, C, M, N, P;

M = (-1,0);
N = (1,0);
C = (0,0);
A = dir(140);
B = dir(20);
P = extension(A, A + rotate(10)*(C - A), B, B + rotate(10)*(C - B));

draw(M--N);
draw(arc(C,1,0,180));
draw(A--C--B);
draw(A--P--B);

label("$A$", A, NW);
label("$B$", B, NE);
label("$C$", C, S);
label("$M$", M, SW);
label("$N$", N, SE);
label("$P$", P, S);
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
d7fee75c-e2e3-5c30-b916-ed909b27975a
task_key
geometry--test--d7fee75c-e2e3-5c30-b916-ed909b27975a
task_revision_id
1
config / split
geometry / test

Official source

initial import