AB is a chord of a circle with centre O. At B, a tangent PB is drawn such that its length is 24cm. The distance of P from centre is 26cm. If the chord AB is 16cm, find its distance from the centre.
Answers
According to the question,
PB = 24cm
PO = 26cm
AB = 16cm
As, we know that when the centre is joined with the tangent is forms 90° with the tangent.
So,
We, will join OB
And,
Angle OBP = 90°
By applying Pythagoras theorem, we get,
OB² + BP² = PO²
OB² = PO² - BP²
OB² = (26)² - (24)²
OB = √676 - 576
OB = √100
OB = 10
So, radius i.e. the distance from the centre = 10cm.
Now, as we now know the radius then we can now find the distance between the cord and the centre of the circle.
Let us make a line OD from centre O to the cord.
Now, by applying Pythagoras theorem, we can find OD
DB = 16/2 = 8cm
OB = 10cm
So,
OD = √(OB)² - (DB)²
= √(10)² - (8)²
= √100 - 64
= √36
= 6cm
So, the distance of cord from the centre = 6 cm
Answer:
Distance of the chord from centre = 6 cm
Step-by-step explanation:
Refer to the attachment
