Geometry Problem

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

Click the figure below to see the complete problem 817.

## Monday, October 22, 2012

### Problem 817: Two Circles, Circumscribed Quadrilaterals, Tangent Lines, Measurement

Labels:
circle,
common tangent,
tangent,
tangential quadrilateral

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EF + AB = BE + AF

ReplyDeleteEF + CD = EC + FD

Adding the two equalities,

2 EF + (AB + CD) = BC + AD

2 EF + 15 = 28

EF = 13/2

In a tangential quadrilateral the sum of opposite sides are equal

ReplyDeleteHence AF + BE = AB + EF and

FD + EC = EF + CD

Adding AD + BC = 2EF + AB + CD

So 28 = 2EF + 15 so EF = 6.5

Sumith Peiris

Moratuwa

Sri Lanka