Question

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

Answer 1

Correct choices are a, b, e

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