Question

Find the length of the tangent to a circle with centre 'O' and radius = 5 cm, from a point Q such that OQ= 13 cm.

• A. 13 cm
• B. 12 cm
• C. 9 cm
• D. 5 cm

Answer 1

The correct option is B 12 cm

By Theorem- The tangent at any point of a circle is perpendicular to the radius through the point of contact.
As, OP is radius and PQ is tangent
$\therefore$ $\angle$ OPQ = ${90}^{\circ }$
Now, consider right-angled $△$ OPQ
By pythagoras theorem,$O{Q}^2=O{P}^2+P{Q}^{2}PQ=\sqrt{O{Q}^2-P{Q}^2}PQ=\sqrt{{13}^2-5^2}PQ=\sqrt{169-25}PQ=\sqrt{144}PQ=\mathrm{12\; cm}$