Question

Learning Task 3: In your answer sheet, copy and answer.
Given: and are tangent and
secant segments, respectively,
of ʘO drawn from exterior point K.
intersects ʘO at N.
Prove: (KL)2 = KM KN
Draw and so that we formed two similar triangles. Then show the
proof using the Two-Column Proof.

Answer 1

Given : KL is tangent  and KMN is secant

To Find : Prove: (KL)² = KM . KN

Solution:

join LM and LN

Compare ΔKLM  and ΔKNL

∠K = ∠K   common

∠KLM = ∠KNL  (  Tangent-Chord Theorem )

=> ΔKLM  ≈ ΔKNL

=> KL/KN  = KM/KL

=> (KL)² = KM . KN

QED

Hence Proved

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