Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 7.2,1 In an isosceles triangle ABC, with AB = AC the bisectors of β π΅ and β C interest each other at O . Join A to O. show that : OB = OC Given: AB = AC OB is the bisector of β B So, β π΄π΅π = β ππ΅πΆ = 1/2 β π΅ OC is the bisector of β C So, β π΄πΆπ = β ππΆπ΅ = 1/2 β πΆ To prove: OB = OC Proof: Since, AB = AC β β ACB = β ABC 1/2β ACB = 1/2β ABC β ππΆπ΅ = β ππ΅πΆ Hence, OB = OC Hence proved Ex 7.2,1 In an isosceles triangle ABC, with AB = AC the bisectors of β π΅ and β π΄ interest each other at O . Join A to O. show that : (ii) AO bisects β π΄. To prove: β OAB= β OAC From part (i) OB = OC β¦(1) Also, In βABO and βACO, we have AB = AC AO = AO OB = OC β΄ β ABO β β ACO β β ππ΄π΅ = β OAC Hence proved

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.