In the figure, Two circles with centres P and Q touch externally at R. Tangents AT and BT meet the common tangent TR at T. If AP = 6 cm and PT = 10 cm, then BT = ?

8 cm

By using pythagoras theorem,

PT² = PA² + AT²

10² = 6² + AT²

AT² = 100 - 36 = 64

AT² = 64

AT = 8 cm

We know, Tangents from a common point to the same circle is of same length,

i.e. TA = TR  & TR = TB

⇒ TA = TR = TB

As, TA = 8 cm

⇒ TB = 8 cm