Section 7.5 Intersecting Chords

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Presentation transcript:

Section 7.5 Intersecting Chords © Copyright all rights reserved to Homework depot: www.BCMath.ca

Review: Similar Triangles When two triangles are similar, then corresponding sides will have the same ratio

I) Property of Intersecting Chords In this section, we will explore three properties of intersecting chords

Property of Intersecting Secants:

Property of Tangent and Secant:

Ex: Solve for “x”: ANS ANS ANS ANS

ANS

Ex: In the diagram, O is the centre of the circle with radius “r” Ex: In the diagram, O is the centre of the circle with radius “r”. ED = “r” and .What is the value of “k”?

CQ Property #2 (Ptolemy’s Thm) Given a CQ with sides a,b,c,d and diagonals x,y

Proof For CQ Property #2 (J.Liu’s Proof) 1st step: Draw a line from point “R” to line ‘y” so that ∕ MRN = ∕ SRT 2ndstep: Find all angles equal to ∕ MRN, or any other angle equal to each other 3rd step: Split “y” to w + z 4th step: Now look for any similar triangles 5th step: Add the two equations

Rewrite the equation to make it easier to prove Now look for similar triangles by showing which angles are equal Now use the formula from the previous slide: