Angles IN and OUT of a Circle On the next 11 slides, copy ALL the information, including the diagrams

CENTRAL ANGLE Define Central Angle: An angle whose vertex is AT the CENTER. Central Angle Formula = the intercepted arc Ex: m<AOC = m AC

INSCRIBED ANGLE Define Inscribed Angle: An angle formed by 2 chords, whose vertex is ON the circle. Inscribed Angle Formula = ½ (intercepted arc) Ex: m<ABC = ½ (mAC)

Inscribed Angle Intercepting a Semi-Circle If an inscribed angle intercepts a semi-circle(which measures 180 degrees), then its measure is half the measure of a semi-circle (which = 90 degrees) Inscribed Angle Intercepting a Semi-Circle = ½(180) = 90 degrees m<ABC = ½ (mAC)

Theorem involving 2 inscribed angles that intercept the same arc When 2 inscribed angles intercept the same arc, the 2 inscribed angles are = and the arc being intercepted is double the inscribed angle. m<A = m<B because they both intercept arc PQ m<P = m<Q because they both intercept arc AB

Angle formed by a Tangent and a Chord An angle formed by a tangent(a line that intersects a circle at 1 point) and a chord(a line segment inside a circle that intersects the circle at 2 points) is equal to half the arc(s) it intercepts. m<CDA = ½ (mCED) m<CDB = ½ (mCD)

Angle formed by 2 Secants Define an angle formed by 2 secants: the angle formed by 2 secants is half the difference of the 2 arcs being intercepted. An angle formed by 2 secants = ½ (larger arc – smaller arc) m<A = ½ (mPS – mNK)

Angle formed by a Tangent and a Secant Define an angle formed by a Tangent and a Secant: the angle formed by a tangent and a secant is equal to half the difference of the 2 arcs being intercepted. An angle formed by a tangent and a secant = ½ (larger arc – smaller arc) m<P = ½ (mAC – mBC)

Angle formed by 2 Tangents Define and angle formed by 2 tangents: An angle formed by 2 tangents is equal to half the difference of the 2 intercepted arcs. m<B = ½ (larger arc – smaller arc) m<B = ½ (mADC – mAC)

Angle formed by 2 Intersecting Chords Define an angle formed by two intersecting chords: An angle formed by 2 intersecting chords is equal to half the sum of the 2 arcs being intercepted. An angle formed by 2 intersecting chords = ½ (arc + arc) m<SVR = ½ (mSR + mTQ) m<TVQ = ½ (mSR + mTQ) AND m<SVT = ½ (mST + mRQ) m<RVQ = ½ (mST + mRQ)

Theorem involving 2 Parallel Chords When you are given 2 parallel chords, mAB = mCD If BC II AD, then mAB = mCD