# Khan/khan-exercises

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 Angle Bisector Theorem
randomTriangleAngles.triangle() [ [ 0, 1 ], [] ] [ [ 1 ], [ 2] ] function(){ var trA = new Triangle( [ 5, -8 ], ANGLES , 14 , {} ); trA.boxOut( [ [ [ 0, -10 ], [ 0, 10 ] ] ], [ 0.4 , 0 ] ); trA.boxOut( [ [ [ 11 , -10 ], [ 11, 10 ] ] ], [ -0.4 , 0 ] ); return trA; }() function(){ var pointD = findIntersection( bisectAngle( TR_A.sides[ 0 ], reverseLine( TR_A.sides[ 2 ] ), 1 ), TR_A.sides[ 1 ] ); return pointD; }() function(){ var trB = new Triangle( [0,0],[], 3, {}, [ TR_A.points[ 0 ], TR_A.points[ 1 ], POINT_D ] ); trB.labels = { "angles" : clearArray( trB.niceAngles, [ 0 ] ), "sides" : mergeArray( clearArray( trB.niceSideLengths, SIDES_B[ 0 ] ), clearArray( [ "?", "?", "?" ], SIDES_B[ 1 ] ) ), "points": [ "A", "B", "D" ] }; return trB; }() function(){ var trC = new Triangle( [0,0],[], 3, {}, [ TR_A.points[ 0 ], POINT_D, TR_A.points[ 2 ] ] ); trC.labels = { "angles" : clearArray( trC.niceAngles, [ 0 ] ) , "sides" : mergeArray( clearArray( trC.niceSideLengths, SIDES_C[ 0 ] ), clearArray( [ "?", "?", "?" ], SIDES_C[ 1 ] ) ), "points": [ "", "", "C" ] }; return trC; }() TR_B.niceSideLengths[ 1 ] TR_B.niceSideLengths[ 0 ] TR_C.niceSideLengths[ 1 ] TR_C.niceSideLengths[ 2 ] TR_B.niceSideLengths[ 1 ] TR_B.niceSideLengths[ 0 ] TR_C.niceSideLengths[ 1 ] TR_C.niceSideLengths[ 2 ]
What is the length of the side AC?
init({ range: TR_A.boundingRange(1.5) }) TR_B.draw(); TR_B.drawLabels(); TR_C.draw(); TR_C.drawLabels();

Angles DAB and DAC are equal.

Therefore AD is the bisector of CAB

Angle Bisector Theorem states that \dfrac{ AB }{ BD } = \dfrac{ AC }{ CD }

roundTo( 1, TEMP_AB * TEMP_CD / TEMP_BD )
What is the length of the side AC? (Round to 1 decimal place).
AC

\dfrac{ AB }{ BD } = \dfrac{ AC }{ CD }

AC = \dfrac{AB \cdot CD }{ BD }

AC = AC

roundTo( 1, TEMP_AC * TEMP_BD / TEMP_CD ) [ [ 1 ], [0] ] [ [ 1,2 ], [ ] ]
What is the length of the side AB? (Round to 1 decimal place).
AB

\dfrac{ AB }{ BD } = \dfrac{ AC }{ CD }

AB = \dfrac{ AC \cdot BD }{ CD }

AB = AB

roundTo( 1, TEMP_AC * TEMP_BD / TEMP_AB ) [ [ 1, 0 ], [] ] [ [ 2 ], [1 ] ]
What is the length of the side CD? (Round to 1 decimal place).
CD

\dfrac{ AB }{ BD } = \dfrac{ AC }{ CD }

CD = \dfrac{ AC \cdot BD }{ AB }

CD = CD

roundTo( 1, TEMP_AB * TEMP_CD / TEMP_AC ) [ [ 0 ], [ 1 ] ] [ [ 1, 2 ], [ ] ]
What is the length of the side BD? (Round to 1 decimal place).
BD

\dfrac{ AB }{ BD } = \dfrac{ AC }{ CD }

BD = \dfrac{ AB \cdot CD }{ AC }

BD = BD

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