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A tangent to a circle is a line intersecting the circle at exactly one point. Can you prove that the line from the center of the circle to the point of tangency is perpendicular to the tangent line?

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

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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?

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