Posted by **Nikki** on Tuesday, April 1, 2008 at 12:35pm.

A circle is circumscribed by a pentagon. The sides are all tangent to the circle. (It's a bit hard to explain without a picture, so I'll do my best.)

The pentagon is QSUWY. However, there are points in between all five sides. In SQ lies point R, SU point T, UW point V, WY point X, and QY with point Z.

It is given that QZ=9, YX=7, XW=12, UW=15, and SU=16. Find the perimeter of the pentagon. In all, I know the perimeter so far is 59, and the problem is I'm not sure how to solve for SQ and ZY. Help please? It's much appreciated.

- Geometry -
**Reiny**, Tuesday, April 1, 2008 at 2:05pm
Even though you did not state it, I will assume that the points R,T,V... are the points of contact of the sides with the circle.

One of the basic properties of tangents and circles is that

If tangents are drawn to a circle from an external point P, and those tangents touch at A and B, then PA = PB

You have that situation 5 times in your figure.

so QZ = QR, YZ= YX, etc.

work your way all around, you will be able to find each segment of the pentagon.

I got 88, but check my arithmetic, I am terrible in arithmetic.

## Answer this Question

## Related Questions

- Geometry - Problem : Howm do you find the area of a circle circumscribed about a...
- Geometry - Bob - Problem : Howm do you find the area of a circle circumscribed ...
- 10th grade - the circle is circumscribed by the pentagon as shown (not drawn to ...
- geometry - A pentagon is a geometric figure with 5 sides. The lengths of the ...
- Multivariable Calculus - A pentagon is formed by placing an isosceles triangle ...
- math - At the Pentagon there are921 feet along each outer side facade and 17.5 ...
- Math - How do you find the value of x for a regular pentagon with its sides ...
- Trigonometry - Find the perimeter of a pentagon circumscribed about the circle ...
- Geometry - Which of the following is true if a pentagon tessellates a plane? a. ...
- geometry - The construction of the regular pentagon is equivalent to the ...

More Related Questions