Question

*The length of tangent segments drawn from an external point to the circle ………….*

1️⃣ are equal
2️⃣ are not equal
3️⃣ sometime equal
4️⃣ are not defined​

Answer 1

Question :- The length of tangent segments drawn from an external point to the circle ………….*

1) are equal

2) are not equal

3) sometime equal

4) are not defined

Answer :- (1) are equal .

Explanation :-

• The tangents drawn from an external point to a circle are of equal length.

Proof :-

in ∆OPT and ∆OQT , we have,

→ OP = OQ {Radius.}

→ ∠OPT = ∠OQT . {Radius is perpendicular to the tangent.}

→ OT = OT { common. }

then,

→ ∆OPT ~ ∆OQT { By RHS. }

therefore,

→ PT = QT { By CPCT. }

Hence, The length of tangent segments drawn from an external point to the circle are equal .

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Answer 2

Given  : The length of tangent segments drawn from an external point to the circle  _______

To Find :  Fill in the blank

1️⃣ are equal

2️⃣ are not equal

3️⃣ sometime equal

4️⃣ are not defined​

Solution:

1️⃣ are equal  is correct answer

The length of tangent segments drawn from an external point to the circle  are equal .

Proof :

Let say O is the center   and P is the external point

PA and PB are tangents

OA = OB = Radius

OP = OP  common

∠OAP = ∠OBP = 90°    ( tangents )

=> ΔOAP ≅ Δ OBP  ( RHS)

=>  PA = PB

Equal tangents

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