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Let ABCD be a trapezoid with bases AB and CD. Let AD=5 and BC=7, and let P be a point on side CD such that CP/DP=7/5. Let X,Y be the feet of the altitudes from P to AD, BC respectively. Show that PX=PY.

 May 28, 2020
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Let ABCD be a trapezoid with bases AB and CD. Let AD=5 and BC=7, and let P be a point on side CD such that CP/DP=7/5. Let X and Y be the feet of the altitudes from P to AD, BC respectively. Show that PX=PY.

 

DC = 12   |   DP = 5   |  CP = 7    |    DM = CN = 4.5    |  AD = 5   |   BC = 7

 

∠ADM = ∠DPX            ∠BCN = ∠CPY     ( See diagram )

 

PX = cos(∠DPX) * DP = 4.5

 

PY = cos(∠CPY) * CP = 4.5

 

 DM = CN = PX = PY    indecision

 

 

 May 28, 2020
edited by Dragan  May 28, 2020
edited by Dragan  May 28, 2020

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