Question 11 of 50intermediate🔧 ApplyDiagram4 marks

Draw ΔABC\Delta ABC with AB=5AB = 5 cm, ∠A=100∘\angle A = 100^\circ, AC=4AC = 4 cm. Draw the circumcircle of ΔABC\Delta ABC. Is the centre inside or outside the triangle?

Correct Answer

The centre of the circumcircle is outside the triangle.

Exercise: Exercise Set 5.1 | Q: 2 | (Page 7)
For More Understanding

Explanation

The textbook context explicitly states that for an obtuse-angled triangle, the circumcentre lies outside the triangle. Since the given angle A is 100 degrees, which is greater than 90 degrees, triangle ABC is an obtuse-angled triangle. Therefore, its circumcentre must lie outside the triangle.

Solution Steps

  1. Step 1: Draw a line segment AB = 5 cm.

  2. Step 2: At point A, construct an angle ∠A = 100°.

  3. Step 3: Along the ray of ∠A, mark point C such that AC = 4 cm. Join BC to complete ΔABC.

  4. Step 4: Draw the perpendicular bisectors of any two sides of the triangle (e.g., AB and BC). Let their point of intersection be O, the circumcentre.

  5. Step 5: With O as the centre and radius equal to OA, draw the circumcircle passing through A, B, and C.

  6. Step 6: Observe the position of O. Since ∠A = 100° makes ΔABC an obtuse-angled triangle, the circumcentre O lies outside the triangle.

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