Question

A cute question - Coordinate geometry

Answer 1

Hmm.. I'm doing this now

Answer 2

that's not cute,looks fearsome, jokin...

Answer 3

If there is a cute solution, then this would be a cute question :)

Answer 4

is BG perpendicular to AC???

Answer 5

if it is, then i think i may have something...

Answer 6

(a)(i) can be done by simply stating:
AngleBAG=AngleBDG
AngleABG=AngleGBD(Incentre is the point of intersection of angle bisectors, so BI bisects angle ABD)

Answer 7

if I is an incenter that means BG is an angle bisector...

Answer 8

@Sarkar, I don't think so. Looks can be deceiving!

Answer 9

that's my line...

Answer 10

so SAS , they're congruent.

Answer 11

This is not a drama! Is my solution clear?

Answer 12

crystal

Answer 13

exactly @dpalnc

Answer 14

So obiviouly Bg is perpendicular to aG.

Answer 15

@dpaInc lol
My workings for ai:
In ΔABG and Δ DBG
∠ABG = ∠ DBC (How should I write the reason?)
BA = BD ( given)
∠BAG = ∠BDG (base ∠, isosΔ)
∴ ΔABG (is congruent to) Δ DBG

Answer 16

*AC

Answer 17

Triangle AI ANd Triangle ABE
Angle ABE = Angle AGI
Angle BAI = IAG
=> SImilar triangles
Proves b

Answer 18

"ABG = ∠ DBC (How should I write the reason?)"
i think you mean angle DBG?

Answer 19

Sorry.. yup...

Answer 20

BG is an angle bisector since BG goes thru the incenter I

Answer 21

Yup.. But how should I present it?
Should it be like this?

since BG goes through the incenter of the triangle, BG is the angle bisector, that is ∠ ABG = ∠ DBG

In ΔABG and Δ DBG
∠ABG = ∠ DBG (proved)
BA = BD ( given)
∠BAG = ∠BDG (base ∠, isosΔ)
∴ ΔABG (is congruent to) Δ DBG

Answer 22

^^ Seems excellent presentation.

Answer 23

i see you're using ASA. that looks fine too.

Answer 24

Oh... I forgot to write ASA ... sorry

Answer 25

@dpaInc another one is AAS, where S is BG=BG ?

Answer 26

Hmm.. G= (-7,0) ?

Answer 27

Yes.

Answer 28

Simple midpoint.

Answer 29

Ad Equation of Circle:
\[(x+7)^2 + (y - 9)^2 = 405\]

Answer 30

I= (-7, 9)?

Answer 31

Yep.

Answer 32

Radii = 9sqrt(5)

Answer 33

Good. I got them all. This one is not a cute one :(

Answer 34

Haha. It's easy. Justl mixed jumbled up to confuse you. Real Charmer.

Answer 35

The key word is incentre... This troubles me :(
I'm not familiar with the centres in a circle