A is a point at a distance 13cm from the center O of a circle of radius 5cm AP - Maths - Circles

Question

A is a point at a distance 13cm from the center O of a circle of
radius 5cm AP & AQ are the tangents to the circle at P&Q If
the tangent BC is drawn at a pont R lying on the minor arc PQ to
intersect AP at B and AQ at C Find the perimeter of ABC?

Manish Bharti · Accepted Answer

BP=BR and CR=CQ ( length of tangents drawn from an external point to a circle are equal )
Perimeter of triangle ABC = AB+BR+RC+CA
=AB+BP+QC+CA
=AP+QA ( AP=QA)
=2AP
In triangle APO, by Pythagoras theorem
$A O^{2} = A P^{2} + P O^{2} 13^{2} = A P^{2} + 5^{2} A P^{2} = 144 \Rightarrow A P = 12$
Perimeter of triangle ABC = $2 \times 12 = 24$ cm

A is a point at a distance 13cm from the center O of a circle of radius 5cm. AP & AQ are the tangents to the circle at P&Q. If the tangent BC is drawn at a pont R lying on the minor arc PQ to intersect AP at B and AQ at C. Find the perimeter of ABC?