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3 years ago

Given: EM, EQ-secantsProve: MP·EW=WQ·EP

Mathematics

1 answer:

Dennis_Churaev [7]3 years ago

7 0

Answer:

Step-by-step explanation:

A secant is a straight line from a point outside a given circle that passes through two points on its circumference.

From the given diagram, EM and EQ are secants.

Thus,

<PEW ≅ <WEP (common angles)

<EMP ≅ <EQW (secant-chord theorem)

<WMP ≅ <PQM (inscribed angles of arc WP)

Therefore,

$\frac{EW}{WM}$ = $\frac{EP}{PQ}$ (corresponding sides of a triangle)

This implies that,

EW*PQ = EP*WM

Therefore,

MP*EW = WQ*EP (properties of a similar triangle)

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