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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
Step 2
|AD| = 10 cm. Work out the length |AB|. Give your answer in cm, in surd form.
Answer
Given that |AD| = 10 cm and triangle ABC is equilateral, we can use trigonometric ratios.
Since angle ADB = 60°, we apply:
ext{Using } an(60°) = rac{AB}{AD} ightarrow AB = AD imes an(60°) ightarrow AB = 10 imes rac{ ext{surd} 3}{1} = 10 ext{surd} 3 ext{ cm}.Step 3
Construct the rest of the Horcrux, using the following facts: (i) The line AD is the perpendicular bisector of [BC].
Answer
- Draw line segment BC.
- Find the midpoint D of BC.
- Using a compass, draw a perpendicular line from D to BC, extending at least to point A.
- Label this line AD.
(ii) The centre of the circle k is the point of intersection of AD and the bisector of the angle at B.
- Using a compass, bisect angle ABC to find the angle bisector.
- Mark the intersection of AD and the angle bisector, labeling it as the center of circle k.
- Draw circle k such that it touches all sides of triangle ABC, ensuring clear construction lines.