Question

5. PT = 2√7 cm, OP=8 cm, find the radius of the circle, if O is the centre
of the circle,​

Answer 1

Answer:

8cm

Step-by-step explanation:

since OP=8cm

Therefore, Radius of the circle is 8cm

Answer 2

Given,

PT=2√7 cm,

OP=8cm,

O is center of the circle.

To Find,

The radius of the circle.

Solution,

Lets take the radius of the circle as x cm

So, radius OB=OA=x cm

now, given that,

OP = 8 cm

We know, OP - OA = AP

⇒(8 - r) = AP

⇒ PA = (8 - r) cm -Equation (1)

and,

Also, PB = PO + OB

⇒PB = (8 + r) cm - Equation (2)

Also, given that,

PT = 2√7 cm - Equation (3)

putting values of Equation (1), Equation (2) and Equation (3) in secant - tangent theorem we get,

PA × PB = PT²

⇒(8 - r)(8 + r) = (2√7)²

Using (a - b)(a + b) = a² - b² in LHS,

⇒(8)² - (r)² = (2)² × (√7)²

⇒64 - r² = 4 × 7

⇒64 - r² = 28

⇒ r² = 64 - 28

⇒r² = 36

⇒ r² = (±6)²

Taking square root both sides,

⇒ r = ± 6 cm

Hence, the radius of the circle is 6 cm.