Answer:
See explanation
Step-by-step explanation:
The given circle has center O.
A, B,C, and D are points on the circumference of the circle.
We want to prove that:
We need to join to B and C as shown in the attachment.
Recall that angle subtended by arc BC at the center is twice the angle subtended at the circumference by the same arc.
This implies that:
The LHS of equation (1) and (2) are equal. Therefore the RHS are also equal.
This implies that:
AC is not perpendicular to XZ, because the slope of AC is -1 and the slope of XZ is 2/3. Hence, the correct answer options are:
B. Is not
A. -1
<h3>How to calculate the slope of any straight line?</h3>Mathematically, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
For the slope of AC, we have:
Point at A = (-1, 3)
Point at C = (4, -2)
Slope, m of AC = (-2 - 3)/(4 - (-1))
Slope, m of AC = (-2 - 3)/(4 + 1)
Slope, m of AC = -5/5.
Slope, m of AC = -1.
For the slope of XZ, we have:
Point at X = (12, 2)
Point at Z = (6, -2)
Slope, m of XZ = (-2 - 2)/(6 - 12)
Slope, m of XZ = -4/-6.
Slope, m of XZ = 2/3.
In Mathematics, a condition that must be met for two lines to be perpendicular is given by this mathematical expression:
m₁ × m₂ = -1
-1 × 2/3 = -1
-2/3 = -1 (False).
Read more on slope here: brainly.com/question/3493733
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<u>Complete Question:</u>
Look at the picture. Then choose the correct option from each drop-down menu.
AC choose..
A. Is
B. Is not
perpendicular to XZ, because the slope of AC is Choose...
A. -1
B. -2
C. 2
D. 1
and the slope of XZ is 2/3
