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Challenge problems: circumscribing shapes

Solve two challenging problems that apply properties of tangents to find the perimeter of a circumscribing shape.

Problem 1

All sides of ABC are tangent to circle P.
A circle centered around point P. The circle is inscribed inside triangle A B C so that each side is tangent to the circle. Side A C is fourteen units. From the tangent point on side A B to point B is sixteen units.
What is the perimeter of triangle ABC?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
units

Problem 2

All sides of quadrilateral ABCD are tangent to circle P.
A circle centered around point P. The circle is inscribed inside quadrilateral A B C D so that each side is tangent to the circle. Side C D is twelve units. From the tangent point on side A B to point B is nine point six units. From the tangent point on side A D to point A is three point seven units.
What is the perimeter of quadrilateral ABCD?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
units

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