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प्रश्न
Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
- What do you call the point O?
- What is the relation between the distances OA, OB and OC?
- Does the perpendicular bisector of BC pass through O?
उत्तर
- O is called the circumcentre of circumcircle of ΔABC.
- OA, OB and OC are the radii of the circumcircle.
- Yes, the perpendicular bisector of BC will pass through O.
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संबंधित प्रश्न
Construct a regular hexagon of side 5 cm. Hence construct all its lines of symmetry and name them.
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Using ruler and compasses only,
- Construct triangle ABC, having given BC = 7 cm, AB – AC = 1 cm and ∠ABC = 45°.
- Inscribe a circle in the ΔABC constructed in (i) above. Measure its radius.
Using ruler and compasses only,
- Construct a triangle ABC with the following data :
Base AB = 6 cm, BC = 6.2 cm and ∠CAB = 60°. - In the same diagram, draw a circle which passes through the points A, B and C and mark its center O.
- Draw a perpendicular from O to AB which meets AB in D.
- Prove that : AD = BD.
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Draw a circle with radius 3 cm and inscribe an equilateral triangle in it.
Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
Does the perpendicular bisector of BC pass through O?
Construct a triangle whose sides are 4.4 cm, 5.2 cm, and 7.1 cm. Construct its circumcircle. Write also the steps of construction.
Construct a ΔABC with base BC = 3.5 cm, vertical angle ∠ BAC = 45°, and median through the vertex A is 3.5 cm. Write also the steps of construction.
Ruler and compasses only may be used in this question. All constructions lines and arcs must be clearly shown, and the be sufficient length and clarity to permit assessment:
(i) Construct a triangle ABC, in which AB = 9 cm, BC = 10 cm and angle ABC = 45°.
(ii) Draw a circle, with center A and radius 2.5 cm. Let it meet AB at D.
(iii) Construct a circle to touch the circle with center A externally at D and also to touch the line BC.
