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CBSE Class 9 Answered

The bisectors of base angles of a triangle cannot enclose a right angle in any case.
Asked by sunilkumarsinha2011 | 07 Jun, 2018, 09:28: AM
answered-by-expert Expert Answer
 
In ΔABC, BP and CP are bisectors of angles B and C respectively.
Hence ∠A + ∠B + ∠C = 180°
∠A + 2∠1 + 2∠2 = 180°
2(∠1 + ∠2) = 180° – ∠A
(∠1 + ∠2) = 90° – (∠A/2) --- (1)
In ΔPBC,
∠P + ∠1 + ∠2 = 180°
∠P + [90° – (∠A/2)] = 180° [From (1)]
∠P = 180° – [90° – (∠A/2)] = [90° + (∠A/2)] 
Hence angle P is always greater than 90°.
Thus PBC can never be a right angled triangle.
Answered by Arun | 07 Jun, 2018, 10:34: AM

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