Help with angles?

Apr 2010
A couple questions (angles, lengths + measures)

Hey! These two questions are stumping me... so I figured I'd come here for some help.

1.) Circle with centre O, CE tangent at D, ∠AOD= 100° , ∠BAD= 48°. Find and explain your answers.

Here's an image I drew up:

And these are the things I need answers for:

a) ∠ODE
b) ∠CDB
c) ∠BOD
d) ∠OBD
e) ∠ADB


2.) Circle with diameter TD and tangents AB, BC, and CA
AR= 5 cm
BS= 9 cm
CS= 17.5 cm

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Here's a drawing I did of it:

Find the numerical value of each of the following:
a) length of AT
b) measure of angle TRD
c) length of RT
d) measure of line segment TD
e) length of AB

Thank you SOO SOOOO much in advance! I REALLY appreciate it!
Dec 2009
Dear Shnub,

Let me give you some ideas,

For the first question, notice that traingle AOD is an isosceles traingle(since OA=OD). Since \(\displaystyle A\hat{O}D\) is given you could find \(\displaystyle O\hat{A}D~and~O\hat{D}A\)

Afterwards using the given angle \(\displaystyle B\hat{A}D=45^O\) you could find \(\displaystyle B\hat{A}O\)

Similarly you could find all angles considering the isosceles traingles, AOB and BOD
Nov 2007
Trumbull Ct
Have you calculated angle OAD as suggested by first reply. If so just proceed to triangles AOB and OBD.
In second problem look up the property of tangents to a circle from an external point.