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Circles, arcs, chords, tangents ...

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Power of the Point

Interesting Fact about Circumference and Area

Big Circle Q

In the accompanying pentgon ABCDE is inscribed in circle o, chords EC and DB intersect at F, chord DB is entended to G and tangent GA is drawn.

Find:

  • mAngle SignBDE
  • mAngle SignBFC
  • mAngle SignAGD
Inscribed Pentago

To solve this probelm, you must remember how to find the meaure of the interior angles of a regular polygon. In the case of a pentagon, the interior angles have a measure of (5-2) •180/5 = 108 °. Therefore, each inscribed angle creates an arc of 216°

Use the inscribed angle formula and the formula for the angle of a tangent and a secant to arrive at the angles

  • mAngle SignBDE = 72 °
  • mAngle SignBFC = 72 °
  • mAngle SignAGD = ½(144 −72) = 36 °

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