Q12 of 50 Page 1

The incircle of an isosceles triangle ABC, in which AB = AC, touches the sides BC, CA and AB at D, E and F respectively. Prove that BD = DC.

Given an isosceles triangle ABC.



Also given AB = AC


So, BF + AF = AE + EC … (1)


From the diagram, AB, BC and CA are tangents to the circle at F, D and E respectively.


⇒ BF = BD, AE = AF and CE = CD … (2)


From (1) and (2),


⇒ BD + AE = AE + CD


⇒ BD = CD


Hence proved.


More from this chapter

All 50 →
10

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

 11

In Figure 1, common tangents AB and CD to the two circles with centres O1 and O2 intersect at E. Prove that AB = CD.


 13

Two different dice are tossed together. Find the probability

(i) That the number on each die is even.


(ii) That the sum of numbers appearing on the two dice is 5.


 14

If the total surface area of a solid hemisphere is 462 cm2, find its volume. [Take π = 22/7]