Q5 of 23 Page 1

Solve Question:

In the given figure, AD is the bisector of the exterior ∠A of Δ ABC . Seg AD intersects the side BC produced in D. Prove that:




Given - Δ ABC is a triangle Ad is exterior bisector of ∠A and meets BC at D


To prove -


Construction: Draw CE∥AD to meet AB at E


Proof -


⇒ In Δ ABC, CE ∥ AD cut by AC


∴ ∠CAD = ∠ACE - - - alternate angles


In ΔABC CE


⇒ In Δ ABC, CE ∥ AD cut by AB


∴ ∠FAD = ∠AEC - - - corresponding angles
∴∠FAD = ∠CAD - - given


∴∠ACE = ∠AEC


AC = AE—isosceles triangle


⇒ In Δ BAD, CE ∥ DA


∴AE = DC


∴AB = BD


But AC = AE



More from this chapter

All 23 →
4

Solve Question:

Eliminate θ, if


x = 3 cosec + 4 cot θ,


y = 4 cosec θ - 3 cot θ.

 4

Solve Question:

A toy is a combination of a cylinder, hemisphere and a cone, each with radius 10 cm as shown in the figure. Height of the conical part is 10 cm and total height is 60 cm. Find the total surface area of the toy.


5

Solve Question:

Construct the circumcircle and incircle of an equilateral ΔXYZ with side 6.5 cm and center O. Find the ratio of the radii of incircle and circumcircle.

 5

Solve Question:

A(5,4). B( - 3, - 2) and C(1, - 8) are the vertices of a triangle ABC. Find the equation of median AD and line parallel to AB passing through point C.