Let ABC be an acute angled triangle whose orthocentre is at H. If altitude from A is produced to meet the circumcircle of triangle ABC at `D` , then prove `H D=4RcosBcosC`

O is the orthocentre of Delta ABC and AD bot BC . If AD is produced it interect the circumcircle of Delta ABC at the point G. Prove that OD= DG .

ABC is an acute angled triangle with circumcenter O and orthocentre H. If AO=AH, then find the angle A.

I is the centre of the incircle of Delta ABC, produced AI intersects the circumercile of that triangle at the point P. Prove that PB=PC=PI

ABC is an obtuse angled triangle whose angle C =135^(@) Value of tanA + cotB is-

Draw a triangle ABC, whose AB = 4.5 cm , BC = 3.5cm and angleABC = 90^@ . Now draw the circumcircle of triangleABC .

In an acute angled triangle ABC, show that tan^2A+tan^2B+tan^2Cge9

ABC is an obtuse angled triangle whose angle C =135^(@) Value of (cot A - 1)(cotB - 1) is

Let ABC be an acute angled triangle with orthocenter H.D, E, and F are the feet of perpendicular from A,B, and C, respectively, on opposite sides. Also, let R be the circumradius of DeltaABC . Given AH.BH.CH = 3 and (AH)^(2) + (BH)^(2) + (CH)^(2) = 7 Then answer the following Value of R is

Find the lengths of chords of the circumcircle of triangle ABC, made by its altitudes__________

ABC is an obtuse angled triangle whose angle C =135^(@) Value of (1 + tan A)(1 + tanB) is-