Question

AB,BC,CA are sides of triangle ABC touch the circle with centre O and radius r at P,Q and R respectively. ( Circle is inside the Triangle and point P is on AB, Q on BC and R on AC ) Prove that - (1) AB+CQ=AC+BQ. (2) Area of ABC = 1/2 Perimeter of ABC * r

22d41a56d8d08e3c93dd5195bbcb64b0.docx

Answer 1

let AB, BC , AC are tanget at P,Q ,R resp.
to prove-1. AB+CQ =Ac+BQ
2.area of ABC =1/2 perimeter of ABC.
Proof- BQ =BP (tangent drwn frm external points are equal)....eqn 1
CQ=CR (do) ... eqn 2
AP=AR (do)...eqn 3
frm 1,2 n 3 we get
AB +CQ =AC +BQ
now,from above we can say that
In triangle ABC,
Area(ABC) = 1/2 x b x h
= 1/2 perimeter of ABC
H/P
hope it helps u !

Answer 2

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Primary SchoolMath 5+3 pts

AB,BC,CA are sides of triangle ABC touch the circle with centre O and radius r at P,Q and R respectively. ( Circle is inside the Triangle and point P is on AB, Q on BC and R on AC ) Prove that - (1) AB+CQ=AC+BQ. (2) Area of ABC = 1/2 Perimeter of ABC * r

Report by Rishitmathur007 29.12.2017

Answers

Mallickpurnananda756 · Helping Hand

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Reeyaa

Reeyaa Ambitious

let AB, BC , AC are tanget at P,Q ,R resp.

to prove-1. AB+CQ =Ac+BQ

2.area of ABC =1/2 perimeter of ABC.

Proof- BQ =BP (tangent drwn frm external points are equal)....eqn 1

CQ=CR (do) ... eqn 2

AP=AR (do)...eqn 3

frm 1,2 n 3 we get

AB +CQ =AC +BQ

now,from above we can say that

In triangle ABC,

Area(ABC) = 1/2 x b x h

= 1/2 perimeter of ABC

H/P

hope it helps u ! Thanks