# Help with angles?

#### Shnub

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: http://i50.tinypic.com/eq44t4.png

And these are the things I need answers for:

a) ∠ODE
b) ∠CDB
c) ∠BOD
d) ∠OBD

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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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AC ┴ AB

Here's a drawing I did of it: http://i49.tinypic.com/2z86bk5.png

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!

#### Sudharaka

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

#### bjhopper

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.

bjh