Question

AC is a transverse common tangent to two circles with centres P and Q and of radio 6 cm and 3 cm. AB = 8cm. Find PQ without using similarity.
(Will mark best answer as Brainliest) ​

Answer 1

Step-by-step explanation:

First of all we should always try to draw the diagram as good as possible and in the above figure AP should be parallel to QC and if u drew the diagram like that it would have helped u a lot I guess.

Also this is a rider and can be done in many ways.Here I present the way which came to my mind after seeing the question(WHILE LYING DOWN ON A COUCH)

NOW COMING TO THE ANSWER

first of all we have to prove that the two triangles are similar.To do these in here we are going to prove that these two triangles(PAB and BCQ) as EQUIANGULAR.

So

angle PAB and BCQ are both equal to 90 degree

again angle PBA and angle CBQ are vertically opposite angles

Now we proved 2 angles as equal hence the third angles must also be equal.

So the two triangles are equianguler hence SIMILAR

Now as we have established that the two triangles are similer we can say that thier corresponding sides are proportional.

so AP/QC=BP/BC

or 6/3=10/BC

and so BC equals to 5 cm

we already know that AB equals to 8 cm and now we just proved that BC equals to 5 cm

therefore AC equals to (AB+BC)=(8+5)cm

which is 13cm

I just solved your math lying on a couch and I am too lazy to get up and do the sum on a piece of paper and post a photo

P.S-PLEASE DO NOT MARK THIS ANSWER AS BRAINLIEST(which I know that I do not deserve).I DONT LIKE TO BE IN THE SPOTLIGHT.