Geometry Problem. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

## Friday, January 20, 2017

### Geometry Problem 1308 Quadrilateral, Diagonal, Triangle, Incircle, Tangent Line, Sides, Measurement

Labels:
geometry problem,
incircle,
quadrilateral,
tangent,
triangle

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Let e= AC and 2p1= perimeter of triangle ABC and 2p2= perimeter of triangle ACD

ReplyDeleteIn triangle ACD we have AF= p2-c= ½(d+c+e)-c

In triangle ABC we have AE= p1-b= ½(a+b+e)- b

X= AF-AE=½(d+c+e)-c-(½(a+b+e)- b)= ½(b+d-a-c)

Let the points of tangency on AB, BC, CD, DA respectively be X,Y,U,V.

ReplyDeleteIf BX = BY = p, AX = AE = a-p, CF = CU = b-p-x.

So DU = DV = c-b+p+x.

Hence AV = d + c - b - p - x = AF = a-p+x

So 2x = d + c - b - a.

Sumith Peiris

Moratuwa

Sri Lanka