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+1 vote
80.3k views
in Mathematics by (53.8k points)
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PB is a tangent to the circle with centre O to B. AB is a chord of length 24 cm at a distance of 5 cm from the centre. If the tangent is of length 20 cm, find the length of PO.

2 Answers

+1 vote
by (17.0k points)
selected by
 
Best answer

Join OB as shown in figure below:

OM = 5 cm

OM ⊥ AB and M is mid-point of AB,

MB = ​\(\frac 12\)AB

= \(\frac 12\) × 24

= 12 cm.

In right-angled triangle △OMB,

OB2 = OM2 + MB2

⇒ OB2 = 52 + 122

⇒ OB2 = 25 + 144

⇒ OB2 = 169

⇒ OB = 169​ cm

OB = 13 cm.

As BP is tangent to circle at B, OB ⊥ BP.

In right-angled triangle △OBP,

OP2 = OB2 + BP2

⇒ OP2 = 132 + 202

⇒ OP2 = 169 + 400

⇒ OP2 = 569

⇒ OP = √569​ cm

Hence, the length of OP = √569​ cm.

+2 votes
by (65.2k points)

Construction meet O to T, To intersect PQ at R.

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