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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 ?

Constructions

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Answer

(i) O is called the incenter of △ABC.

(ii) From figure,

OR and OQ are radius of incircle.

Hence, OR = OQ.

(iii) OC is the bisector of angle C.

∴ ∠ACO = ∠BCO.

Hence, ∠ACO = ∠BCO.

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 ? Constructions, Concise Mathematics Solutions ICSE Class 10.

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