Question

Question no 17 plz and quickly . that question which has 'o' if a center...... Etc or a option in 17the question

Answer 1

In triangles OMA and OMB

OM =OM (Common)

MA = MB (M is mid point of AB)

OA = OB (Radii of same circle)

Hence

triangle OMA is congruent to triangle OMB (By SSS Rule)

Therefore angle OMA = angle OMB (By CPCT)----equation 1

ALSO

angle OMA +angle OMB =180 degrees (linear pair)

2×angle OMA = 180 degrees (from equation 1)

angle OMA =90 degrees or OM is perpendicular to AB

Hope it helps

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Answer 2

given- a circle with center o ,

AB is a chord of a circle

AM=BM

∴OM bisects the chord AB

to prove- OM IS pERpendicular to AB

proof- in triangle AOM & BOM

OA = OB (radii of the same circle)

OM =OM (common side)

AM = BM (given)

∴ TRIANGLE AOM is congruent to BOM

∠AMO =∠ BMO

AMO+BMO=180 (LPA)

2AMO=180

∴ AMO=90

ie. OM is perpendicular to AB

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