From an external point P, tangents PA and PB are drawn to a circle of radius 5 units with - Maths - Circles

Question

From an external point P, tangents PA and PB are drawn to a circle
of radius 5 units with centre O , where A and B are the points on
the circle If PA = 12 units then find:
(A) area of quadrilateral PAOB
(B) area of triangle PAB
(C) radius of circumcircle of triangle PAB

Anuradha Sharma · Accepted Answer

Hi,
<img src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ana_qa_image_58c286480586a%20png">

here OA= OB = 5 and PA=PB= 12OP= 52+122= 13so area of PAOB = 2×area of triangle PAO= 2×12×5×12= 60 SQUARE UNIT now since OA= 5 so using pythagrus triplet OM = 3 and AM = 4 so PM= 13-3 = 10So area of PAB = 12×AB×PM=12×8×10 = 40 square unitnow since angle A+angle B= 180 = angle APB+angle AOBhence circum center of triangle APB will pass through O
 So OP will be diameter and hence radius = 132= 6
5 unitRegards

From an external point P, tangents PA and PB are drawn to a circle of radius 5 units with centre O , where A and B are the points on the circle . If PA = 12 units then find: (A) area of quadrilateral PAOB (B) area of triangle PAB (C) radius of circumcircle of triangle PAB

From an external point P, tangents PA and PB are drawn to a circle of radius 5 units with centre O , where A and B are the points on the circle . If PA = 12 units then find:
(A) area of quadrilateral PAOB
(B) area of triangle PAB
(C) radius of circumcircle of triangle PAB