Advertisements
Advertisements
प्रश्न
The sides AB and AC of a triangle ABC are produced; and the bisectors of the external angles at B and C meet at P. Prove that if AB > AC, then PC > PB.
योग
उत्तर
In ΔABC,
AB > AC,
⇒ ∠ACB < ∠ABC
⇒ 180° - ∠ACB < 180° - ∠ABC
∠BCE < ∠DBC
`("∠BCE")/2 < ("∠DBC") /2`
∠BCP < ∠CBP
In ΔBCP
∠BCP < ∠CBP
⇒ BP < CP
⇒ PC > PB
shaalaa.com
Inequalities in a Triangle - If two sides of a triangle are unequal, the greater side has the greater angle opposite to it.
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
Prove that the straight line joining the vertex of an isosceles triangle to any point in the base is smaller than either of the equal sides of the triangle.
In the following figure, ABC is an equilateral triangle and P is any point in AC;
prove that: BP > PA
From the following figure; 
prove that:
(i) AB > BD
(ii) AC > CD
(iii) AB + AC > BC.
