Answer: Draw radii PA and PB with ∠APB = 100° and draw perpendiculars to them at A and B; these are the tangents (they meet at 80°).
Analysis: The measure of a minor arc equals its central angle, so \(\angle APB = 100^\circ\).
Steps of construction:
- Draw a circle with centre P and any convenient radius, say 3 cm. Draw radius PA.
- With the protractor draw \(\angle APB = 100^\circ\) with B on the circle. Arc AB (minor arc) measures \(100^\circ\).
- Draw rays PA and PB. Through A draw line \(l \perp\) ray PA, and through B draw line \(m \perp\) ray PB.
- Lines \(l\) and \(m\) are the required tangents.
If they meet at T, then in quadrilateral PATB, \(\angle ATB = 360^\circ - 90^\circ - 90^\circ - 100^\circ = 80^\circ\).