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.

Answer 1

True choices are 1, 2, 5

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:

1. AC = BC

• Correct, both equal to r

2. AC = BD

• Correct, both equal to r

3. 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

4. ABCD is a square

• Incorrect. ACBD is rhombus

5. ABD is an equilateral triangle

• Correct, all three sides are equal to r

6. CD = AB + AB

• Incorrect as CD = AB√3