Mathematics
Two circles 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.
Answer
We know that,
If two tangents are drawn to a circle from an exterior point, the tangents are equal in length.
From figure,
Q is the point from which, QA and QP are two tangents to the circle with centre O
So, QA = QP ……….(1)
Similarly, from point Q, QB and QP are two tangents to the circle with centre O’
So, QB = QP ……….(2)
From (1) and (2), we have
QA = QB
Hence, proved that the tangents are equal.
Related Questions
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Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner.
In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If AB = 15 cm and AC = 7.5 cm, calculate the radius of the circle.
