Properties of Centres and Coordinates of Orthocentre

In the figure, AB = BC. I is the incentre of ∆ABC. Find ∠ABC and ∠AIC.

• ∠ABC = 35 degrees, ∠AIC = 110 degrees

• ∠ABC = 40 degrees, ∠AIC = 110 degrees

• ∠ABC = 75 degrees, ∠AIC = 120 degrees

• ∠ABC = 40 degrees, ∠AIC = 125 degrees

In the figure, AEC, AHD, BDC and BHE are straight lines. H is the orthocentre of ∆ABC. Find x and y.

• x = 15 degrees,

  y = 75 degrees

• x = 18 degrees,

  y = 72 degrees

• x = 20 degrees,

  y = 70 degrees

• x = 25 degrees,

  y = 65 degrees

In the figure, ADB, AHE, BEC and CHD are straight lines. H is the orthocentre of ∆ABC. Find ∠ABC.

• 70 degrees

• 120 degrees

• 75 degrees

• 60 degrees

In the figure, BDC is a straight line. O is the circumcentre of ∆ABC. OD ⊥ BC. Find BC.

• 34 cm

• 15 cm

• 16 cm

• 30 cm

In the figure, H is the orthocenter of △ABC. Write down the x-coordinate of H.

• 0

• 2

• 4

• -4

In the figure, H is the orthocenter of △ABC. Find the y-coordinate of H.

• -3

• 0

• 2

• 5

Find the slope between two points : (-1, 0) and (2, 3)

• -1

• 1

• 3

• -3

The slope of AB is -2. If PQ is perpendicular to AB, find the slope of PQ.

• -2

• 2

• 1/2

• -1/2

Given two points A(2, 0) and B (3, 3). If PQ is perpendicular to AB, find the slope of PQ.

• 3

• -3

• 1/3

• -1/3

In the figure, H is the orthocenter of △ABC. Find the coordinates of H.

• (1, 2.5)

• (0, 2)

• (2, 0)

• (0, 1.5)