Question

if ab is a chord of a circle with Centre O and P is the midpoint of BA what is angle OPA​

Answer 1

Answer:

   RL003Maths AryaBhatta

Heya,

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 2

Answer:

angle OPA will be a right angle as the line from the centre bisects the chord at 90 degrees