Question

In the fig., find PO'. If PA = 12 cm and O'B = 5 cm.
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Answer 1

Answer:

it is gicen that PA =12cm and O'B=5cm.

PA=PT=PB=12cm ( tangents to the same exterior point are equal in length)

Let O'P be x cm.

using pythagoras theoram,

as angle O'BP= 90° (PB is the tangent)

(O'P)² = (O'B)² +(PB)²

x²= 5²+ 12²

x²= 25+ 144

x²= 169

x= 13 cm

hence, O'P= 13cm

Answer 2

The length of PO' is 13cm

GIVEN

PA = 12 cm and O'B = 5 cm.

TO FIND

The value of PO'.

SOLUTION

We can simply solve the above problem as follows;

It is given.

PA = 12cm

O'B = 5cm

We know that,

PA = PT = PB = 12cm (Tangents of circles from a common exterior points are equal in length)

Let us assume the length of PO' = xcm

We know that,

∠O'BP = 90°

PB is a tangent to the circle with centre O'.

Applying Pythagorus Theoram in ΔO'BP

(PO')² = (O'B)² + (PB)²

x² = 5² + 12²

= 25 + 144

x² = 169

x = √169

x = 13cm

Hence, The length of PO' is 13cm

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