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This diagram is a straightedge and compass construction. A is the center of one circle, and B
is the center of the other. Select all the true statements.
a. AC = BC
b. AC = BD
C. CD = AB
d. ABCD is a square
e. ABD is an equilateral triangle
f. CD = AB + AB

This diagram is a straightedge and compass construction A is the center of one circle and B is the center of the other Select all the true statements a AC BC b class=

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mhanifa

Answer:

Correct choices are a, b, e

Step-by-step explanation:

As per diagram, the circles are equal.

Since the distance AB is the radius of both circles:

  • AB = AC = BC = BD = AD = r

So the answer choices:

a. AC = BC

  • Correct, both equal to r

b. AC = BD

  • Correct, both equal to r

C. CD = AB

  • Incorrect. Half of CD is the leg of 30-60-90 triangle and is equal to  r√3/2, so CD = AB√3

d. ABCD is a square

  • Incorrect. ACBD is rhombus

e. ABD is an equilateral triangle

  • Correct, all three sides are equal to r

f. CD = AB + AB

  • Incorrect as CD = AB√3
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