ab is a chord of length 16cm of a circle of radius 10 cm the tangents at a and - Maths - Circles

Question

ab is a chord of length 16cm of a circle of radius 10 cm the
tangents at a and b intersect at point p find the length of pa

Ayush Jha · Accepted Answer

We have the following situation

OA =10 cm Perpendicular from centre to the chord bisects the chord So AM = MB = 8cm Using Pythagoras Theorem in triangle AOM $O M = \sqrt{10^{2} - 8^{2}} = 6 c m$ So, $\tan ∠ A O M = \frac{8}{6} = \frac{4}{3}$ Now in triangle OAP $\tan ∠ A O M = \frac{P A}{O A} \frac{4}{3} = \frac{P A}{10} P A = \frac{40}{3} c m$

ab is a chord of length 16cm of a circle of radius 10 cm .the tangents at a and b intersect at point p.find the length of pa