Question

Arc BC is a semicircle with segment BC as diameter ,O is the centre of semicircle and OM is perpendicular to AC at point M. Prove that point M is the midpoint of AC.​

Answer 1

Answer:

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Step-by-step explanation:

so here Angle CMO=Angle CAB=90 degrees

so here both Angle CMO and Angle CAB forms a pair of corresponding angles

so we know that

If the corresponding angles are congruent then the lines are parallel

so hence

we can conclude that

OM || AB

now here O is centre of semicircle

thus then

BO=OC (radii of same semicircle) (1)

now since

OM || AB

By Basic Proportionality Theorem

We get

MC/AM=OC/BO

MC/AM=OC/OC from (1)

ie MC=AM

so as MC and AM are equidistant from point A

we can say that

M is midpoint of AC (by definition of midpoint )

thus proved