Question 10 of 50intermediate🔧 ApplyDiagram4 marks

Draw ΔABC\Delta ABC with AB=5AB = 5 cm, ∠A=70∘\angle A = 70^\circ and ∠B=60∘\angle B = 60^\circ. Draw the circumcircle of ΔABC\Delta ABC. Is the centre inside or outside the triangle?

Correct Answer

(Construction) 1. Draw a line segment AB = 5 cm. 2. At point A, draw a ray making an angle of 70° with AB. 3. At point B, draw a ray making an angle of 60° with AB, intersecting the previous ray at point C. 4. Draw the perpendicular bisectors of sides AB and BC. Let them intersect at point O. 5. With O as the centre and radius OA, draw the circumcircle of ΔABC.

(Position of Centre) Inside the triangle

Exercise: Exercise Set 5.1 | Q: 1 | (Page 7)
For More Understanding

Explanation

To determine the position of the circumcentre, we first find the third angle of the triangle: ∠C = 180° - (70° + 60°) = 50°. Since all three angles (70°, 60°, 50°) are less than 90°, ΔABC is an acute-angled triangle. The textbook context states that for an acute-angled triangle, the circumcentre lies inside the triangle. Therefore, the centre of the circumcircle is inside ΔABC.

Solution Steps

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

  2. Step 2: Construct ∠A = 70° and ∠B = 60°. Their intersection is point C.

  3. Step 3: Calculate ∠C = 180° - (70° + 60°) = 50°.

  4. Step 4: Draw perpendicular bisectors of AB and BC intersecting at O.

  5. Step 5: Draw circumcircle with centre O and radius OA.

  6. Step 6: Conclude that the centre O is inside the triangle because it is an acute-angled triangle.

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