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Home > GC > Chapter 10 > Lesson 10.1.5 > Problem 10-52

10-52.

A line, e, x, is tangent to a circle, with center, o, and radius, o, x, at the point, x. Line segment, from, o, to, e, intersects the circle at point, n.In the figure at right, is tangent to at point . cm and cm.

 

  1. What is the area of the circle?

    According to the definition of the tangent line, what is the measure of ?
    How can you use this to find the length of ?

    A tangent line is perpendicular to a radius, so the measure of , so the triangle is a right triangle. So we can use the Pythagorean Theorem.

  1. What is the area of the sector bounded by and ?

    Find the measure of . Use this to find the area of the sector.

  2. Find the area of the region bounded by , , and .

    Find the area of the triangle formed by . Subtract the area of the sector from the area of the triangle.