Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Official Geometry Topic (For evene)

I have revised it to make more sense.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Official Geometry Topic (For evene)

Yes Bob, I like the diagram.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Official Geometry Topic (For evene)

I need some vital hints with these problems. I already spent like 45 minutes figuring this one out. So yeah, I'm tired

has side lengths

,

, and

. Let

be the intersection of the angle bisector of

with side

, and let

be the foot of the perpendicular from

to side

. Compute the length of

.

Last edited by evene (2015-11-25 02:40:51)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Official Geometry Topic (For evene)

Hi;

I am getting 72 / 19.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Official Geometry Topic (For evene)

Thanks, that is correct!

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Official Geometry Topic (For evene)

You get the idea... Need help with this, need help with that... blah blah bleh!

Triangle ABC is inscribed in equilateral triangle PQR, as shown. If PC = 3, BP = CQ = 2, and

, then compute AQ.

In a triangle ABC, take point D on

such that DB = 14, DA = 13, DC = 4, and the circumcircles of triangles ADB and ADC have the same radius. Find the area of triangle ABC.

Last edited by evene (2015-11-25 07:53:49)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Official Geometry Topic (For evene)

hi evene,

Q2.

This has taken a while.  I think this works:

Construct the perpendicular bisectors of AD, BD and DC.  The circumcentres are at the intersections so I've marked these as E and F.

H is the midpoint of BD, G of DC.  I've also drawn JK parallel to BC through A

As FD = ED, the line AD bisects that isosceles triangle, and GHKJ is a rectangle (shaded yellow).

Area ABC = half base x height = 0.5 x BC x HK.  But as H and G are midpoints 0.5 x BC = GH, so the shaded rectangle is the same area as ABC. 

We know one side (GH) and can calculate the other like this.

A perpendicular from point A to BC will meet BC at L (not shown).  Triangle ALD is right angled with AD = 13, and LD = 7-2 = 5.  So you can use Pythagoras to calculate AL and hence complete the question.

Q1

Triangle ABC is inscribed in equilateral triangle PQR, as shown. If PC = 3, BP = CQ = 2, and
, then compute AQ.

I think I need more information as there is no diagram.  Please say which side each of A, B and C is.  eg.  B is on PR.
Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Official Geometry Topic (For evene)

Don't mind Q1, I just finished solving. I got

is equal to

.