Mathematics
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.
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