AB is a chord of length 16cm of circle of radius 10cm the tangents at A and B intersect at point P. Find the length of PA.

Open in App

Solution

AT = TB (perpendicular from centre bisect the chord)
$Δ A O T, O T = \sqrt{10^{2} - 8^{2}} = 6$
$Δ P A O, ∠ O A P = 90^{\circ}$
$∠ A O P = t a n θ = \frac{P A}{O A}$ ....(i)
$Δ A O T, ∠ A O T = t a n θ = \frac{A T}{O T} = \frac{8}{6}$ ..(ii)
So, from (i) and (ii)
$\frac{8}{6} = \frac{P A}{10}$ $∴ P A = \frac{40}{3} c m$

Suggest Corrections

Similar questions

In the given figure, AB is a chord of length $16 c m$ of the circle of radius $10 c m$ . The tangents at A and B intersect at point P. Find the length of PA.

Q. In figure

A B

is a chord of length

16 c m

of a circle of radius

10 c m

. The tangents at

A

and

B

intersect at a point

P

. Find the length of

P A

In Fig. $8.63$ , $A B$ is a chord of length $16 c m$ of a circle of radius $10 c m$ . The tangents at $A$ and $B$ intersect at a point $P$ . Find the length of $P A$ .