Question

Find the radius of the circle with centre O. PT is a tangent and AB is perpendicular to PT. PA and PB is 4 cm and 2 cm respectively.

• A. 4 cm
• B. 2 cm
• C. 6 cm
• D. 3 cm

Answer 1

The correct option is C

6 cm

Using Pythagoras theorem,

$P{T}^2$​+ $O{T}^2$​​ = $P{O}^2$

$(2+r{)}^2+r^2=(4+r{)}^2$​

$4+r^2+4r+r^2=16+8r+r^2$

$r^2-4r-12=0$

$r^2-6r+2r-12=0$

$r(r-6)+2(r-6)=0$

$(r+2)(r-6)=0$

r = 6 and -2

r = 6 [because distance can’t be negative]