Q12 of 105 Page 612

In the given figure, if AB = AC, prove that BE = CE.

We know, that tangents drawn from an external point are equal.


AD = AF


[tangents from point A] [1]


BD = BE


[tangents from point B] [2]


CF = CE


[tangents from point C] [3]


Now,


AB = AC [Given] …[4]


Substracting [1] From [4]


AB - AD = AC - AF


BD = CF


BE = CE [From 2 and 3]


Hence Proved.


More from this chapter

All 105 →
10

Prove that the lengths of two tangents drawn from an external point to a circle are equal.

 11

Prove that the tangents drawn at the ends of the diameter of a circle are parallel.

 13

If two tangents are drawn to a circle from an external point, show that they subtend equal angles at the center.

 14

Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.