Wednesday

April 16, 2014

April 16, 2014

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

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 2:05pmEven 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.

**Related Questions**

Geometry - Problem : Howm do you find the area of a circle circumscribed about a...

circle geometry triangles - how do u construct a circle that is circumscribed of...

Geometry - Bob - Problem : Howm do you find the area of a circle circumscribed ...

geometry - In the diagram, circle A is tangent to circle C, and segment BE is ...

geometry - For "circle"(O,r) , AP is the tangent at "A belongs to circle", from ...

geometry - consider a circle of radius 1, and corresponding inscribed and ...

geometry - consider a circle of radius 1, and corresponding inscribed and ...

GEOMETRY CIRCLE - 1.An isosceles triangle with each leg measuring 13 cm is ...

GEOMETRY CIRCLES PLEASE - 1.An isosceles triangle with each leg measuring 13 cm ...

Please help with circle tangents geometry - Two circles of different sizes are ...