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

10-52.

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.

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.