Question

Examine the diagram of circle D, where two chords, JL¯¯¯¯¯¯¯ and FH¯¯¯¯¯¯¯¯, are equidistant from D. Segment BC is a diameter of circle D and bisects JL¯¯¯¯¯¯¯ and FH¯¯¯¯¯¯¯¯ at points K and G, respectively.

The diagram as described in the problem.


Which statements are true?

Select all that apply.

1. m∠FCG=90∘
2. ∠JKB≅∠FGC
3. m∠BKL=90∘
4. ∠BKL≅∠FCG

Answer 1

Statement 1 and statement 4 are true, while statement 2 and statement 3 are false.

Step-by-step explanation:

To determine which statements are true, we need to analyze the given information. We know that chords JL and FH are equidistant from the centre of circle D, which means that chords JL and FH are parallel to each other.

1. Statement 1 is true. Since chords JL and FH are parallel and BC is a diameter, angle FCG is a right angle.

2. Statement 2 is false. There is no direct relationship between angles JKB and FGC.

3. Statement 3 is false. Since angle FCG is a right angle, angle BKL cannot also be a right angle, as that would make triangle BKL a right triangle.

4. Statement 4 is true. Angle BKL is congruent to angle FCG, as they both form the same angle at the centre of the circle.