In the given figure, `DeltaABC` is an equilateral triangle whose side BC has been produced in both the directions to D and E respectively. Prove that `/_ACD=/_ABE`.

In the given figure, DeltaABC is an equilateral triangle of side 3 units. Find the coordinates of the other two vertices.

BC is an equilateral triangle. A circle is drawn with centre A so that it cuts AB and AC at points M and N respectively. Prove that BN = CM

In the given figure BC is produced on both sides to points D and E respectively. Find the values of x and y

In the given figure ABC is a triangle and D is the mid-point of BC. AD is produced to E. BM and CN are two perpendiculars dropped from B and C respectively on AE. Prove that : DeltaBMD~=DeltaCND

In the given figure ABC is a triangle and D is the mid-point of BC. AD is produced to E. BM and CN are two perpendiculars dropped from B and C respectively on AE. Prove that : BM=CN

In DeltaABC, AB = AC and the bisectors of angleB and angleC meet AC and AB at point D and E respectively. Prove that BD = CE .

The given figure shows an equilateral triangles ABC and D is point in AC. Prove that : (i) AD lt BD (ii) BC gt BD

In the given figure DeltaABC is equilateral on side AB produced. We choose a point such that A lies between P and B. We now denote 'a' as the length of sides of DeltaABC , r_1 as the radius of incircle DeltaPAC and r_2 as the ex-radius of DeltaPBC with respect to side BC. Then r_1 + r_2 is equal to

In each of the following figures, one side of a triangle has been produced. Find all the angles of the triangle in each case.

ABC is a triangle A line is drawn parallel to BC to meet AB and AC in D and E respectively. Prove that the median through A bisects DE.