There are two circles each with radius 5 cm. The length of tangent AB is 26 cm. Find the length of tangent CD.
24 cm
From the figure shown above,
AB = PO = 26 cm
Consider triangle CQP and DQO
∠ CQP = ∠ DQO (Vertically opposite angles)
∠ PCQ = ∠ODQ = 90∘ (Line joining the center to the tangent at the point of contact of the circle)
PC = OD (radius is equal)
therefore the two triangles are congruent using AAS postulate
PQ=QO=262=13 cm
Similarly CQ = QD
Consider triangle PCQ,
Applying Pythagoras Theorem, we get,
CQ2+CP2=PQ2
CQ2+52=132
CQ2 = 132 – 52=144
CQ = 12 cm
Therefore, CD = 2CQ = 24 cm