Triangles and circumference: "Given a circle with center O and radius r, draw a chord AB...."

[AM797]

Hello everyone!
I need your help to solve two problems if you can:

1. Given a circle with center O and radius r, draw a chord AB and the tangents to the circle at points A and B, which intersect at point C. Determine the distance of chord AB from the center such that the ratio of the area of triangle ABC to the area of the rectangle with sides AB inscribed in the circle is 3/4.

2. In an isosceles triangle ABC with base AB, the base measures 10a, and the radius of the inscribed circle is 10/3a. Determine the perimeter of the triangle. Draw the bisector BD of angle ABC (angle at B) and determine the lengths of segments AD, DC, and MD, knowing that M is the point of tangency on side AC of the triangle.

Thank you in advance!

 

[stapel]

I need your help to solve two problems if you can:

1. Given a circle with center O and radius r, draw a chord AB and the tangents to the circle at points A and B, which intersect at point C. Determine the distance of chord AB from the center such that the ratio of the area of triangle ABC to the area of the rectangle with sides AB inscribed in the circle is 3/4.

2. In an isosceles triangle ABC with base AB, the base measures 10a, and the radius of the inscribed circle is 10/3a. Determine the perimeter of the triangle. Draw the bisector BD of angle ABC (angle at B) and determine the lengths of segments AD, DC, and MD, knowing that M is the point of tangency on side AC of the triangle.

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Thank you!

 

[Steven G]

Your first step will be to draw a graph. Have you done that? Can we see your labelled graph?

 

[khansaheb]

1. Given a circle with center O and radius r, draw a chord AB and the tangents to the circle at points A and B, which intersect at point C. Determine the distance of chord AB from the center such that the ratio of the area of triangle ABC to the area of the rectangle with sides AB inscribed in the circle is 3/4.

Hint: (1) Draw a rough sketch of the circle, the tangents, the chord and the rectangle. Label the sketch according to the "given" of the problem.

(2) Now in terms of that sketch - describe the the "FIND" of the problem mathematically.