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MATH / In circle J, HO and HN are tangent to the circle at O and N. Find the number of degrees in the sum of m∠J and m∠H. [asy] size(150); import graph; pair J = (0,0), H = (6,0), O, N; p…

Problem

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problem

In circle JJ, HOHO and HNHN are tangent to the circle at OO and NN. Find the number of degrees in the sum of m∠Jm\angle J and m∠Hm\angle H. [asy] size(150); import graph; pair J = (0,0), H = (6,0), O, N; path circ = Circle(J,3); pair M = midpoint(J--H); path secCirc = Circle(M,3); pair[] tangentPoints = intersectionpoints(circ,secCirc); O = tangentPoints[0]; N = tangentPoints[1]; draw(J--N--H--O--cycle); draw(circ); label("HH",H,E); label("JJ",J,W); label("NN",N,S); label("OO",O,NE); [/asy]
Plain-text mathematical notation (without MathML)
In circle J, HO and HN are tangent to the circle at O and N. Find the number of degrees in the sum of m∠J and m∠H. [asy]
size(150);
import graph;
pair J = (0,0), H = (6,0), O, N;
path circ = Circle(J,3);
pair M = midpoint(J--H);
path secCirc = Circle(M,3);
pair[] tangentPoints = intersectionpoints(circ,secCirc);
O = tangentPoints[0]; N = tangentPoints[1];
draw(J--N--H--O--cycle);
draw(circ);
label("H",H,E);
label("J",J,W);
label("N",N,S);
label("O",O,NE);
[/asy]
Original LaTeX notation
In circle $J$, $HO$ and $HN$ are tangent to the circle at $O$ and $N$. Find the number of degrees in the sum of $m\angle J$ and $m\angle H$. [asy]
size(150);
import graph;
pair J = (0,0), H = (6,0), O, N;
path circ = Circle(J,3);
pair M = midpoint(J--H);
path secCirc = Circle(M,3);
pair[] tangentPoints = intersectionpoints(circ,secCirc);
O = tangentPoints[0]; N = tangentPoints[1];
draw(J--N--H--O--cycle);
draw(circ);
label("$H$",H,E);
label("$J$",J,W);
label("$N$",N,S);
label("$O$",O,NE);
[/asy]

level

Level 1

type

Geometry

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Source and history

task_id
6ecd16e0-1b33-514d-a9f9-5e028d48183c
task_key
geometry--test--6ecd16e0-1b33-514d-a9f9-5e028d48183c
task_revision_id
1
config / split
geometry / test

Official source

initial import