Question
Bisectors of angles and of a triangle intersect its circumcircle at and respectively. Prove that the angles of the triangles are , and .
Found 5 tutors discussing this question
Discuss this question LIVE
14 mins ago
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
Was this solution helpful?
150
Share
Report
One destination to cover all your homework and assignment needs
Learn Practice Revision Succeed
Instant 1:1 help, 24x7
60, 000+ Expert tutors
Textbook solutions
Big idea maths, McGraw-Hill Education etc
Essay review
Get expert feedback on your essay
Schedule classes
High dosage tutoring from Dedicated 3 experts
Practice questions from similar books
Question 1
If a vertex of a triangle is
, and the middle points of two sides passing through it are
and
then find the centroid and the incenter of the triangle.Question 2
Find the locus of a point, so that the join of
and
subtends a right angle at the moving point.Stuck on the question or explanation?
Connect with our math tutors online and get step by step solution of this question.
231 students are taking LIVE classes
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 |