Question

Abc is a triangle in which ab = 4 cm, bc = 5 cm and ac = 6 cm. A circle is drawn to touch side bc at p, side ab extended at q and side ac extended at r. Then, aq equals :

Answer 1

Answer:

aq = 7.5 cm

Step-by-step explanation:

It is given that,

Abc is a triangle in which ab = 4 cm, bc = 5 cm and ac = 6 cm. A circle is drawn to touch side bc at p, side ab extended at q and side ac extended at r.

From the figure attached with this shows that,

aq and ar are the 2 tangent to the circle from common point a

Therefore aq = ar

Similarly, bq = bp and cp = cr

Let bp = 'x' and cp = 5 - x (since bc = 5 given)

therefore bq = x and cr = 5-x

We have, aq = ar

aq = ab + bq  = 4 + x and ar = ac + cr = 6 + (5 - x)

4 + x = 6 + (5 - x)

2x = 6 + 5 - 4 = 7

x = 7/2 = 3.5 cm

Therefore aq = ab + bq  = 4 + x = 4 + 3.5 = 7.5