Question:medium
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
Updated On: Jan 13, 2026
- 12 cm
- 13 cm
- 8.5 cm
- \(\sqrt {119}\) cm
Show Solution
The Correct Option is D
Solution and Explanation
Given \(PQ^2 =144 - 25\), we know that the line from the center of the circle to the tangent is perpendicular to the tangent. Therefore, \(OP \perp PQ\). Applying the Pythagorean theorem in \(\text {ΔOPQ}\), we have:
\(OP^2 + PQ^2 = OQ^2\)
\(5^2 + PQ^2 =12^2\)
\(25 + PQ^2 =144\)
\(PQ^2 =144 - 25\)
\(PQ^2 =119\)
\(PQ = \sqrt {119} \text{ cm}\)
The correct option is (D): \(\sqrt {119} \text{ cm}\)
Was this answer helpful?
0
Top Questions on Tangent to a Circle
- How many tangents can a circle have?
- CBSE Class X
- Mathematics
- Tangent to a Circle
- Fill in the blanks :
- A tangent to a circle intersects it in ____ point(s).
- A line intersecting a circle in two points is called a ____ .
- A circle can have ____ parallel tangents at the most.
- The common point of a tangent to a circle and the circle is called ____ .
- CBSE Class X
- Mathematics
- Tangent to a Circle
- Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.
- CBSE Class X
- Mathematics
- Tangent to a Circle
- A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see Fig. 10.14). Find the sides AB and AC.
Fig. 10.14 - CBSE Class X
- Mathematics
- Tangent to a Circle
- Want to practice more? Try solving extra ecology questions todayView All Questions