Question
Bisectors of angles and of a triangle intersect its circumcircle at and respectively. Prove that the angles of the triangles are , and .
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Text solutionVerified
In ,
But ....angle addition property
Now, and .....Angles inscribed in the same arc
[Since is bisector of and is bisector ]
....(1)
Similarly, and ...(2)
Now, ....angle sum property of triangle
...(3)
Similarly, and ...(4)
Substituting eq (3) in eq (1), we get
Similarly, and
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Question Text | Bisectors of angles and of a triangle intersect its circumcircle at and respectively. Prove that the angles of the triangles are , and . |
Answer Type | Text solution:1 |
Upvotes | 150 |