Question

6. Please help. What is the length of BC⎯⎯⎯⎯⎯⎯⎯⎯? Enter the correct value.

Answer 1

Answer: 47

=================================================

Work Shown:

Connect points A and B with a line segment. Through the HL (hypotenuse leg) congruence theorem, you can prove triangle ABC is congruent to triangle ABD. From there, using CPCTC (corresponding parts of congruent triangles are congruent) we know that BC = BD.

In short: tangents from an external point are the same length.

------

BC = BD

-2x+85 = 5x-48

85+48 = 5x+2x

133 = 7x

7x = 133

x = 133/7

x = 19

-----

Use this x value to find the length of BC

BC = -2x+85

BC = -2(19)+85

BC = -38+85

BC = 47

and let's check BD as well. It should also be 47 units long.

BD = 5x-48

BD = 5*19-48

BD = 95-48

BD = 47

This confirms our answer.

Answer 2

Answer:

The answer is 47, they are correct.