Question

Prove!!!

❌Don't Spam

Answer 1

ANSWER :

GIVEN :

in circle at centre O

AB and AC are chords such that

angle BAD =angle DAC

ALSO AD is a diameter

TO PROVE :

AB = AC

CONSTRUCTION :

DRAW OF perpendicular to AB

and OE perpendicular to AC

PROOF :

NOW in ∆OAF and ∆OAE

angle OAF = angle OAE.........( Given)

also angle OFA = angle OEA......(Construction)

also OA=OA .....(Common side)

so by AAS congruence criteria

∆OAF is congruent to ∆OAE

so by CPCT

AF = AE......1

Now

by the theorem perpendicular drawn on a chord of a circle bisect the chord

AF=BF=AB/2.....2

AND

AE=EC=AC/2......3

SO By putting 2 and 3 in 1

we get

AB/2= AC/2

=> AB= AC

HENCE PROVED

NOTE :

while solving such questions

try to think about the construction required

Answer 2

Hope this attachment will help you....Nandini