Question

in the following figure, PQ and pr are tangents to a circle with the centre O. Line segment AC touches the circle at point B.

(i) state the relation between tangents PQ and PR.
(ii) PQ = PA + AB
(iii) PR = PC + CB
(iv) PQ + PR = perimeter of triangle PAC

Answer 1

(i) PQ=PR theorem-10.2

(ii)PQ=PA+AQ....1️⃣

AQ=AB.... 2️⃣. thm-10.2

From-2️⃣ in 1️⃣

PQ=PA+AB

(iii) similar as (ii)

(iv) Perimeter of =Sum of all sides.

Perimeter of PAC=PA+PC+AB+BC

from 2️⃣ and CR=CB

Perimeter of PAC=PA+PC+AQ+CR

=PQ+PR