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# Tangents

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In the diagram, AB and AD are the two tangent lines of circle O that go through A. We know ∠C = 4∠A. Find the degree measure of arc BCD.

Two circles, centered at O1 and O2, are externally tangent to each other, and tangent to a line ` at T1 and T2, respectively. The radii of circle O1 and circle O2 are x and y, respectively. Find T1T2 in terms of x and y

Two circles O1 and O2 are tangent to each other, and the radius of circle O1 is 1. Points A, B, P are such that P lies on line O1O2, PA is tangent to circle O1 at A, PB is tangent to circle O2 at B, and A is the midpoint of PB. Find the length PO1

In the diagram shown, PC is tangent to the circle and PD is the angle bisector of ∠CPE. If arc CD = 70◦ , arc DE = 30◦ , and ∠DQE = 40◦ , then determine arc AE (the arc below AE).

Feb 22, 2021

### 2+0 Answers

#1
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1. arc BCD is 80 degrees.

2. T1T2 = (x + y)/xy

3. PO1 = 3.

4. arc AE is 65 degrees.

Feb 22, 2021
#2
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Could you please explain how you got it?

Guest Feb 22, 2021