Mathematics
Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
(i) What do you call the point O ?
(ii) What is the relation between the distances OA, OB and OC ?
(iii) Does the perpendicular bisector of BC pass through O ?
Related Questions
Using ruler and compasses only,
(i) Construct a triangle ABC with the following data :
Base AB = 6 cm, BC = 7.5 cm and angle CAB = 60°.
(ii) In same diagram, draw a circle which passes through the points A, B and C and mark its center O.
(iii) Draw a perpendicular from O to AB which meets AB in D.
(iv) Prove that : AD = BD.
The bisectors of angles A and B of a scalene triangle ABC meet at O.
(i) What is the point O called ?
(ii) OR and OQ are perpendiculars drawn to AB and CA respectively. What is the relation between OR and OQ ?
(iii) What is relation between angle ACO and angle BCO ?
Using ruler and compasses only construct a triangle ABC in which BC = 4 cm, ∠ACB = 45° and perpendicular from A on BC is 2.5 cm. Draw a circle circumscribing the triangle ABC.
(i) Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm and CA = 5 cm.
(ii) Find its incenter and mark it I.
(iii) With I as centre, draw a circle which will cut off 2 cm chords from each side of the triangle.