BY K.NIRMALA DEVI KV AFS, BEGUMPET GEOMETRY BY K.NIRMALA DEVI KV AFS, BEGUMPET

Q.1 In ∆ ABC BP ┴ AC, BM is median, BN is bisector of . Prove that

Q. 2. P is any point on the minor arc BC of the Q.2 P is any point on the minor arc BC of the circumcircle of an equilateral ∆ ABC. Then prove that AP = BP + CP.

Q. 3. Prove that distance of orthocentre from the vertex Q.3 Prove that distance of orthocentre from the vertex of a triangle is double the distance of the circumcenter from the side.

In an equilateral triangle the circumcentre, In an equilateral triangle the circumcentre, incentre, orthocentre and centroid coincide. In an isosceles triangle the circumcentre, incentre, orthocentre and centroid are collinear. In a scalene triangle the cicumcentre, orthocentre, and centroid lie on the same line and centroid divides this line in the ratio 2:1. This line is called Euler’s line.

Q. 4. If H is the orthocentre and O is the circumcentre Q.4 If H is the orthocentre and O is the circumcentre of a ∆ ABC, then prove AH / OM = 2/1.

Q. 5. In ∆ ABC, F is the midpoint of AC. E is a point Q.5 In ∆ ABC, F is the midpoint of AC. E is a point on BC such that BE = 2EC then find BQ/QF.

Q. 6. ABCD is a square. A line through B intersects Q.6 ABCD is a square. A line through B intersects CD produced at E, the side AD at F and the diagonal AC at G. If BG = 3 and GF = 1 then find the length of FE.

Q. 7. In a parallelogram ABCD prove that sum of Q.7 In a parallelogram ABCD prove that sum of squares of the sides is equal to the sum of squares of its diagonals.