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प्रश्न
Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
What is the relation between the distances OA, OB and OC?
उत्तर
OA, OB and OC are the radii of the circumcircle.
APPEARS IN
संबंधित प्रश्न
Using a ruler and compasses only:
1) Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ABC = 120°
2) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.
3) Measure ∠BCP.
Construct a triangle ABC in which base BC = 6 cm, AB = 5.5 cm and ∠ABC = 120°.
Construct a circle circumscribing the triangle ABC.
Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.
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, draw an equilateral triangle of side 5 cm. Draw its inscribed circle. Measure the radius of the circle.
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?
Using ruler and compasses only, construct Δ ABC in which BC=7.5 cm, ∠ ABC = 60° and AC - AB= 1.5 cm. Inscribe a circle in the Δ ABC and measure its radius.
In triangle ABC, ∠ABC = 90°, AB = 6 cm, BC = 7.2 cm and BD is perpendicular to side AC. Draw circumcircle of triangle BDC and then state the length of the radius of this circumcircle drawn.
Construct an isosceles triangle ABC such that AB = 6 cm, BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Find the points Q and R which are 5 cm from P and also 5 cm from the line AB.
Construct a Δ ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.
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.
