Question

In the figure 6.21. CD is a diameter
of the circle with centre 0. Diameter
CD is perpendicular to chord AB at
point E Show that A ABC is an
isosceles triangle.​

Answer 1

Answer:

Answer:

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Given : CD is the diameter with centre O , CD perpendicular to chord AB at point E

To prove : triangle ABC IS isoceles triangle

Solution : IN triangle ABC ,

OE is perpendicular to AB so

AE = EB.....(1).....perpendicular drawn from the centre of the circle to a chord bisects the chord

Angle CEA = CEB..... (2)....CE IS PERPENDICULAR

SIDE CE=CE. ....(3)....SAME SIDE

THEREFORE , FROM 1 , 2 AND 3

CAE = CBE ....BY SAS TEST

THEREFORE CA=CB....(4)...C.S.C.T.

From (4)...TRIANGLE ABC IS ISOCELOUS TRIANGLE , HENCE PROVED

Answer 2

from ∆ OAB, OA and OB is same as radious of one cercle.

From ∆OEA and ∆OEB

1. OA=OB
2. angle OEA and angle OEB is equal is 90°
3. OE is common .

that's we proved ∆OEA is simmilar to ∆OEB

then all simmilar part of two ∆ are simmilar

so,AE is equal to BE.

Also from ∆CEA and ∆CEB

1. OE is common
2. AE=BE
3. angle CEA = angle CEB=90°

So from above we can get AC is equal to AB

Hence proved ∆ABC is a isosceles Tringle.