Question

24. In the adjoining figure 'O' is the
centre of a circle and CE = DE.
Prove that OE // GD.
​

Answer 1

Given :- In the adjoining figure 'O' is the centre of a circle and CE = DE.

To Prove :- OE || GD .

Construction :-

• Join CD, OD .
• Extend OE such that it cuts CD at M .

Solution :-

In ∆CDG,

→ ∠CDG = 90° { Angle in semi - circle . }

so,

→ GD ⊥ CD -------- Eqn.(1)

now,

→ OC = OD { Radius of circle.}

so, ∆OCD is an isosceles ∆ .

also,

→ CE = ED { given. }

then, E will be centroid of isosceles ∆OCD .

therefore,

→ OM ⊥ CD { Median of isosceles ∆ is perpendicular to the base. } ------------- Eqn.(2)

Hence, from Eqn.(1) and Eqn.(2)

→ OE || GD { since corresponding angles are equal.} (Proved.)

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Answer 2

Answer:

Step-by-step explanation: