CAT 2008: Quantitative Questions a Day 51-100 -The discussions-Brought to you by SMOT

[jasleen_kaur]

QQAD 106 :the answer is option (c)

[jasleen_kaur]

Originally Posted by bmanasa

i dint understand this part of the question...
is he talking about..the circle being a tangent here...
or it is that AB is the tangent to the circle at D..if so ,how??

AB is the tangent to the circle at D..well its inscribed inside it. a circle is drawn inside the triangle ABC and touching side AB of it at D

[bhargava2008]

Can anyone post a detailed explanation for Q) 106

[jasleen_kaur]

Let in triangle ABC the incircle meet AB at D, BC at F and AC at E.

Case 1: AB = AC

Now CE^2 = 6√2*3√2 = 36 => CE = CF = 6,
Also in an isosceles triangle AF will contain the incentre, circumcentre , centroid and orthocentre.
=> AF will bisect BC hence BF = 6 = BD.

In triangle CDB BD = 6 CD = 6√2 and BC = 12,
=> cos(< B) = 3/4 -> FB / AB = 3/4 -> AB =8.
=> the perimeter is 28 and angle A is obtuse (square of the largest side is greater than sum of square of other 2 sides) so it is an obtuse angled triangle. So (2) and (4) are true here.

Case 2: When AC = BC

we already have CE = BF = 6 and CD is also perpendicular to AB. Let AD = AE = a, applying pythagorean
theorem for triangle ADC, we get a = 3 => AC = BC = 9, and AB = 6
=> (1) and (3) are also true.
=> Choice (5) is the right answer

[rajsuryan]

Hi frenz..

CAn I get all these questions compiled at one place.?
plz help me if any1 has it..

[explorehims]

hey......what about the pair (3,4)

(3^2 + 1)*(4^2 + 1) = (13^2 + 1)

Hence clearly the answer is not the first option.

Please tell me if i'm wrong!!