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Tangent and Secant Lines

Tangent and Secant Lines: Level 2 Challenges


Given the quadrilateral and inscribed circle, what is the missing side length?

In the figure given above TP\overline{TP} and TQ\overline{TQ} are tangent to the circle with center OO at BB and C,C, respectively.

If PBA=60\angle PBA=60^\circand ACQ=70\angle ACQ=70^\circ, what is BTC\angle BTC in degrees?

There is a semi-circular object on a road and a strong metal plate is put on it, as shown in the above diagram, so that cars can better pass over it. If the radius of the object is 2828 inches and the angle between the plate and the road is 30,30^\circ, what is the distance (in inches) between the point the plate meets the road and the point the plate touches the semi-circular object?

A point PP is given outside of a circle Γ\Gamma . A tangent from PP touches Γ\Gamma at TT with PT=45PT=45. A line from PP cuts Γ\Gamma at the 2 points A,BA, B. If PA=25PA=25, what is the length of PBPB?

In the above diagram, line segment PT\overline{PT} is tangent to both circle OO and circle O.O'. Given the following three lengths: AB=35,PC=30,CD=20,\lvert\overline{AB}\rvert = 35, \lvert\overline{PC}\rvert = 30, \lvert\overline{CD}\rvert = 20, what is PA?\lvert\overline{PA}\rvert?


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