Exercise 46 Page 767

Practice makes perfect

Let's start by paying close attention to the triangle in the given diagram.

Note that KL is a radius and JK is tangent to the circle. According to the Tangent to a Circle Theorem, the angle formed by them is a right angle. Also, the triangle is a right triangle.

We can see that the lengths of the legs are 4 and x. The length of the hypotenuse is 5. If we substitute these values in the equation of the Pythagorean Theorem, we will be able to find the value of x. Let's do it!

a^2+b^2=c^2

SubstituteValues

Substitute values

4^2+ x^2= 5^2

▼

Solve for x

CalcPow

Calculate power

16+x^2=25

SubEqn

LHS-16=RHS-16

x^2=9

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x = 3

We only take the positive root of x^2 since the length of the segment cannot be negative. Therefore, the value of x is 3.

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Exercises p.763-767

Exercise 46 Page 767

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