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  • AB is a direct common tangent of two circles of radii p and q touching each other externally. Then the value of AB2Option: 1 pq</

AB is a direct common tangent of two circles of radii p and q touching each other externally. Then the value of AB2

Option: 1

pq


Option: 2

2pq


Option: 3

3pq


Option: 4

4pq


Answers (1)

best_answer

LET AB be the direct common tangent, OA = p and BI = q

Let T be any point on line AI such that OI || BT

then, BI = OT = q

AT = p - q

TB = p + q

ATB is a right angle triangle   

Apply Pythagoras theorem

\\BT^2=AT^2+AB^2\\AB^2=BT^2-AT^2\\\mathrm{\;\;\;\;\;\;\;}=(p+q)^2-(p-q^2)=4pq

Posted by

Kuldeep Maurya

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