Tangent and Secant Lines
Given the quadrilateral and inscribed circle, what is the missing side length?
by
Souryajit Singh
In the figure given above \(\overline{TP}\) and \(\overline{TQ}\) are tangent to the circle with center \(O\) at \(B\) and \(C,\) respectively.
If \(\angle PBA=60^\circ\)and \(\angle ACQ=70^\circ\), what is \(\angle BTC\) in degrees?
by
Mehul Chaturvedi
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 \(28\) inches and the angle between the plate and the road is \(30^\circ,\) what is the distance (in inches) between the point the plate meets the road and the point the plate touches the semi-circular object?
by
Jimin Khim
A point \(P\) is given outside of a circle \(\Gamma \). A tangent from \(P\) touches \(\Gamma\) at \(T\) with \(PT=45\). A line from \(P\) cuts \(\Gamma\) at the 2 points \(A, B\). If \(PA=25\), what is the length of \(PB\)?
by
Calvin Lin
In the above diagram, line segment \(\overline{PT}\) is tangent to both circle \(O\) and circle \(O'.\) Given the following three lengths: \[\lvert\overline{AB}\rvert = 35, \lvert\overline{PC}\rvert = 30, \lvert\overline{CD}\rvert = 20,\] what is \(\lvert\overline{PA}\rvert?\)
by
Souryajit Singh