Complete the following theorem: The line drawn from the centre of a circle to the midpoint of a chord is .. - NSC Technical Mathematics - Question 7 - 2019 - Paper 2

To find angle AĂ, we use the property that the sum of the angles in a triangle equals 180°:

$AĂ + CĂI + AEB = 180°$ Substituting the known values: $AĂ + 26.6° + 90° = 180°$ Solving for AĂ gives: $AĂ = 180° - 26.6° - 90° = 63.4°$

Since angle BĮ lies in a semicircle, we have:

$BĮ = 90° - 26.6° = 63.4°$

Therefore, angle BĮ is also 63.4°.

The length of AE is given as:

$AE = 4 ext{ units}$

The length of ED can be expressed as:

$ED = 5 - x ext{ units}$

To find the numerical value of x, we can use the Pythagorean theorem in triangle AOE:

Using the relationship: $AO^2 = AE^2 + OE^2$ Substituting values: $8^2 = 4^2 + x^2$ $64 = 16 + x^2$ Solving: $x^2 = 64 - 16 = 48$ $x = ext{√}48 = 4 ext{√}3 ext{ or } x = 3$. Thus, the numerical value of x is 3.