<p>Match the Columns: Given triangle ABC with specific properties, match the characteristics with their corresponding values.</p>
Step-by-Step Solution
Key Concept: The orthocentre of a triangle coincides with the incentre of its medial or related triangle in special configurations.
<p><strong>Step 1:</strong> Identify the orthocentre H of triangle ABC and the incentre of triangle DEF.</p><p><strong>Step 2:</strong> Calculate the inradius of triangle ABC: \(r_{ABC} = \frac{4}{2\sqrt{3}} = \frac{2\sqrt{3}}{3}\)</p><p><strong>Step 3:</strong> Calculate the inradius of triangle DEF: \(r_{DEF} = \frac{1}{\sqrt{3}}\)</p><p><strong>Step 4:</strong> Verify that the orthocentre H of triangle ABC is the incentre of triangle DEF at \(H \equiv \left(0, \frac{1}{3}\right)\)</p><p>∴ Answer is a-p, b-s, c-q, d-r.</p>
Correct Answer: a-p, b-s, c-q, d-r