Math Is Fun Forum

Oran2009

Member

Registered: 2016-06-13

Posts: 21

Circle Geometry Problems

1) Let

,

, and

be points on a circle. Let

and the tangent to the circle at

intersect at

. If

,

, and

, then find

.

2) In triangle

,

,

, and

. Let

be the point on the circumcircle of triangle

so that

. Find

.

Please help!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Circle Geometry Problems

Hi;

---

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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Circle Geometry Problems

Last edited by thickhead (2016-07-09 16:19:32)

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Circle Geometry Problems

hi Oran2009

Q1.

There is a theorem (ask if you want the proof) that says that AB.AC = AD.AD so that makes AC = 16 and so you can get AC by Pythagoras.

Bob

---

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Circle Geometry Problems

hi Oran2009

Here's a method for Q2:

My software (Sketchpad) has called point P, point D because it letters in sequence.

As ABC is right angled, AB is a diameter with E as centre.  And F is the 'foot' of the perpendicular from  A to CD (CP).

CF is easy to calculate as CFA has a 90 and a 45 degree angle and is isosceles.

Angle CBA = CDA by angles subtended by the same chord, so triangles ABC and ADF are similar.  So you can calculate FD by ratios.

Bob

---

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

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Circle Geometry Problems

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}