Find radius if a circle is inscribed in quadrilateral

In summary, the conversation is discussing a math problem involving a circle with a diameter of 25cm and the relationship between the various lines and angles within the circle. The person being addressed is asked to show their work and use their own thoughts to solve the problem before seeking help. Hints are given to guide them towards the correct solution.
  • #1
amitdixit
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  • #2
Hey amitdixit and welcome to the forums.

What have you tried? What have you already thought about?
 
  • #3
you need to show some work before we can help.

To give you a hint the answer it isn't a) since the diameter would be 22cm but DC is 25cm do you see why?

Next hint is that br=bq and lines that are tangent to the circle are perpendicular to the radius drawn there so you can construct some intermediate triangles and test the other possible answers.
 

1. What is the formula for finding the radius of a circle inscribed in a quadrilateral?

The formula for finding the radius of a circle inscribed in a quadrilateral is:
r = (ab)/(a+b+c), where a, b, and c are the sides of the quadrilateral.

2. How do you determine the center of the inscribed circle in a quadrilateral?

The center of the inscribed circle in a quadrilateral can be found by drawing the diagonals of the quadrilateral and finding their intersection point. This point will be the center of the inscribed circle.

3. Can the radius of a circle inscribed in a quadrilateral be negative?

No, the radius of a circle cannot be negative. It represents the distance from the center of the circle to any point on its circumference, and distance cannot be negative.

4. Is the radius of a circle inscribed in a quadrilateral always equal to the inradius?

Yes, the radius of a circle inscribed in a quadrilateral is always equal to the inradius. Inradius is the term used for the radius of a circle inscribed in any polygon, including a quadrilateral.

5. How does the size and shape of a quadrilateral affect the radius of the inscribed circle?

The size and shape of a quadrilateral can affect the radius of the inscribed circle. Generally, the larger the quadrilateral, the larger the inscribed circle's radius will be. Also, the more symmetric the quadrilateral is, the closer the inscribed circle's radius will be to the inradius.

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