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Since the slanted sides are tangent to each roller, \(\angle\,ODA = \angle\,PEC =90^\circ \). Will the goalie have to move farther to block a shot toward the right goalpost R or the left goalpost L Solution The congruent angles tell you that the goalie is on the bisector of ZLBR. The length \(OB\) will then be simple to determine. Solve a real-world problem EXAMPLE 2 SOCCER A soccer goalie's position relative to the ball and goalposts forms congruent angles, as shown. To do this, we will show that \(\triangle\,OBC\) is a right triangle, then find the angle \(\angle\,BOC \), and then find \(BC \). The diameter \(d\) of the large roller is twice the radius \(OB \), so we need to find \(OB \). Find the diameter \(d\) of the large roller, given the information in the diagram. Each roller touches both slanted sides of the V-block. The machine tool diagram on the right shows a symmetric V-block, in which one circular roller sits on top of a smaller circular roller. We did exactly that in Examples 1.14, 1.15, and 1.16. Solving Word Problems Using Block Models Label Variables Jamie spent 40 for an outfit. When the problem contains a circle, you can create right angles by using the perpendicularity of the tangent line to the circle at a point with the line that joins that point to the center of the circle. There is no general strategy for this, but remember that a right triangle requires a right angle, so look for places where you can form perpendicular line segments. Often no right triangle will be immediately evident, so you will have to create one. In applied problems it is not always obvious which right triangle to use, which is why these sorts of problems can be difficult. For example, in the situation pictured above, the robot might unstack C from A and then unstack A from B and. A Blocks World program is a schedule of observations and actions. You may have noticed that the solutions to the examples we have shown required at least one right triangle. In order to unstack a block, that block must be clear of other blocks and, in order to stack one block on another, both blocks must be clear. Note: This answer is close to the sun's actual (mean) radius of \(432,200\) miles.