#### Question

Two circle touch each other externally at point P. Q is a point on the common tangent through P. Prove that the tangents QA and QB are equal.

#### Solution

From Q, QA and QP are two tangents to the circle with centre O

Therefore, QA = QP.....(i)

Similarly, from Q, QB and QP are two tangents to the circle with centre O'

Therefore, QB = QP ......(ii)

From (i) and (ii)

QA = QB

Therefore, tangents QA and QB are equal.

Is there an error in this question or solution?

Solution Two Circle Touch Each Other Externally at Point P. Q is a Point on the Common Tangent Through P. Prove that the Tangents Qa and Qb Are Equal. Concept: Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments.