1.

Which of the following given statement(s) is / are TRUE?In a ∆ABC, ∠A = 70° and I, O, H and X are incentre, circumcentre, orthocentre, and ex-centre of triangle, respectively.A: ∠BIC = 105°B: ∠BOC = 140°C: ∠BHC = 120°D : ∠BXC = 55°1. A, B and D2. A and D3. B and D4. B, C and D

Answer» Correct Answer - Option 3 : B and D

GIVEN:

Four statements.

CONCEPT:

Geometry

FORMULA USED:

∠BIC = 90° + (∠A / 2)

∠BOC = 2 × ∠A

∠BHC = 180° - ∠A

∠BXC = 90° - (∠A / 2)

CALCULATION:

A:

∠BIC = 90° + (∠A / 2)

= 90° + (70° / 2)

= 90° + 35°

= 125°

B:

∠BOC = 2 × ∠A

= 2 × 70°

= 140°

C:

∠BHC = 180° - ∠A

= 180 - 70°

= 110°

D:

∠BXC = 90° - (∠A / 2)

= 90° - (70° / 2)

= 90° - 35°

= 55°

Hence, only B and D are TRUE.


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