The diagram below shows a Horcrux - Junior Cycle Mathematics - Question 12 - 2018
Question 12
The diagram below shows a Horcrux.
ABC is an equilateral triangle. D is the midpoint of [BC]. AD is perpendicular to BC.
The circle k touches the three sides of ABC.... show full transcript
Worked Solution & Example Answer:The diagram below shows a Horcrux - Junior Cycle Mathematics - Question 12 - 2018
Step 1
Write the correct transformation into the box below. Be as specific as you can.
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Answer
“ABD is the image of ACD under axial symmetry in the line AD.”
Step 2
|AD| = 10 cm. Work out the length |AB|.
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Answer
Using trigonometry, we can set up the relation:
∣AB∣=sin60∘10
Calculating this gives:
∣AB∣=2310=320 cm
Thus, the final answer in surd form is:
∣AB∣=3203 cm
Step 3
Construct the rest of the Horcrux, using the following facts:
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Answer
Start by drawing triangle ABC with sides AB, BC, and AC equal.
Locate point D on line BC such that AD is perpendicular to BC. This ensures that D is the midpoint of segment BC.
To find the center of circle k, construct the bisector of angle B.
Where line AD intersects the bisector of angle B is the center of circle k.
Clearly mark all points and the circle that touches the sides of triangle ABC.
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