Chapter 12 Review Brett Solberg AHS ‘11-’12

Warm-up 1)Solve for x 2) Solve for x Turn in CRT review and extra credit. Have 12.4 out for HW check and questions.

HW Review

Today’s Agenda CH 12 Review Ch 12 Test EC WS What you need to know for the test Ch 12 Test 14 Questions EC WS

Theorem 12-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

Example 1 BA is tangent to Circle C at point A. The measure of angle B is 22˚. Find the value of x.

Example ML and MN are tangent to circle O. Find the value of x.

Inscribed/Circumscribed Inscribed Circle – A circle which is tangent to all the sides of a polygon. Circumscribed Circle – A circle which is tangent to all the vertices of a triangle.

Theorem 12.3 2 segments tangent to a circle from a point outside the circle are congruent.

Example Circle C is inscribed by XYZW. Find the perimeter of XYZW.

Theorem 12.6 In a circle, a diameter that is perpendicular to a chord bisects the chord and its arc.

Example 4 Solve for the missing side length.

Inscribed Circle Inscribed Angle Intercepted arc Angle whose vertex is on a circle and whose sides are chords. Intercepted arc Arc created by an inscribed angle.

Theorem 12.9-Inscribed Angle Theorem The measure of an inscribed angle is half the measure of its intercepted arc. ABC = ½AC x x 𝒙 𝟐

Example 2 Find the measure of arc PT and angle R.

Example 2 Find the measure of angle G and angle D.

Theorem 12.10 The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.

Example 4 RS and TU are diameters of circle A. RB is tangent to circle A at point R. Find the measure of angle BRT and TRS.

Theorem 12.11 Part 1 The measure of an angle formed by 2 lines that intersect inside a circle is the average of the 2 arcs. angle 1 = x+y 2

Example Find the value of x.

Theorem 12.11 Part 2 The measure of an angle formed by 2 lines that intersect outside a circle is the difference of the arcs divided by 2. x−y 2 x is the bigger angle

Example Find the value of x.

Theorem 12.12 Part 1 If two chords intersect, then a∙b=c∙d.

Example Find the value of x.

Theorem 12.2 Part 2 If 2 secant segments intersect, then (w + x)w = (z + y)y

Example Find the value of x.

Theorem 12.2 part 3 If a secant segment and a tangent segment intersect, then (y + z)y = t2

Example Find the value of z.

Test Good Luck!