Answer based on the following diagram.From " $P$ '' tangents PA and PB are drawn. $C A = B C = r a d i u s$ and E is the mid point of AB. If $P A = A B = 6$ units, what is the length of radius if $C E = \sqrt{3}$ units.

\sqrt{3}

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3

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2 \sqrt{3}

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6

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Solution

The correct option is C $2 \sqrt{3}$
Join C to the midpoint of AB, let's say E
Then, $C E ⊥ A B$ and $A E = B E = \frac{6}{2} = 3$ units.

In $Δ A C B$ ,
$B C = A C =$ radius and $C E ⊥ A B$
$C E^{2} + A E^{2} = A C^{2}$
$\Rightarrow 3 + 9 = A C^{2}$
$\Rightarrow A C = 2 \sqrt{3}$ units

SO, option C is correct.

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Answer based on the following diagram.From "P'' tangents PA and PB are drawn. CA=BC=radius and E is the mid point of AB. If PA=AB=6 units, what is the length of radius if CE=√3 units.

The correct option is C 2√3Join C to the midpoint of AB, let's say EThen, CE⊥AB and AE=BE=62=3 units.In ΔACB, BC=AC= radius and CE⊥ABCE2+AE2=AC2⇒3+9=AC2⇒AC=2√3 unitsSO, option C is correct.

Answer based on the following diagram.From " $P$ '' tangents PA and PB are drawn. $C A = B C = r a d i u s$ and E is the mid point of AB. If $P A = A B = 6$ units, what is the length of radius if $C E = \sqrt{3}$ units.