Question

A tangent to a circle at the point P from A is 24cm long. If O is the centre of the circle and OA = 26 cm, find the diameter of the circle.

Answer 1

OA=26cm

<OPA=90°

AP=24cm

OP=√(OA^2-PA^2)

=√(676-576)

=√(100)

=10

Radius=10 Cm

Diameter=2r=20Cm

Answer 2

HELLO DEAR,

[ figure is in the attachment]

now,
$\sf{GIVEN:-}$ PA = 24CM , OA = 26CM.

IN ∆ APO , <P = 90°

so, by Pythagoras theorem

OA² = PO² + PA²

(26)² = PO² + (24)²

(26)² - (24)² = PO²

PO² = (26 - 24)(26 + 24)

PO² = 2(50)

PO² = 100

PO = 10cm

HENCE, diameter of circle = 2×PO

so, diameter = 2×10cm = 20cm.

I HOPE ITS HELP YOU DEAR,
THANKS