document.write( "Question 1190528: Solve the problem and show the solutions.\r
\n" ); document.write( "\n" ); document.write( "The measure of the angle formed by two tangents to a circle is 80 degrees. Find the measure of the intercepted arc. \n" ); document.write( "

Algebra.Com's Answer #822204 by ikleyn(52864) $\"\"$ $\"About$

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\n" ); document.write( "Solve the problem and show the solutions.
\n" ); document.write( "The measure of the angle formed by two tangents to a circle is 80 degrees.
\n" ); document.write( "Find the measure of the intercepted arc.
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document.write( "Make a sketch.\r\n" );
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document.write( "In the sketch, find two right-angled triangles.\r\n" );
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document.write( "    (As a reminder, the radius drawn to the tangent point is a perpendicular to the tangent line).\r\n" );
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document.write( "In these triangles, you are given that the acute angles at the vertex outside the circle are half of 80 degrees, each,\r\n" );
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document.write( "i.e. 40 degrees.\r\n" );
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document.write( "    (As a remainder, the line connecting the point outside the circle with its center is the bisector \r\n" );
document.write( "     of the angle between the tangent lines to the circle from this point).\r\n" );
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document.write( "Therefore, two central angles at the center of the circle are 90 - 40 = 50 degrees each.\r\n" );
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document.write( "It implies that the central angle intercepting the arc is the sum 50 + 50 = 100 degrees.\r\n" );
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document.write( "ANSWER.  The intercepted arc is 100 degrees.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "For properties of tangent lines to a circle, which I used in the solution, see the lessons\r
\n" ); document.write( "\n" ); document.write( " - A tangent line to a circle is perpendicular to the radius drawn to the tangent point \r
\n" ); document.write( "\n" ); document.write( " - Tangent segments to a circle from a point outside the circle \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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