9. A tangent is drawn from a point at a distance of 17 cm of circle of radius 8
cm. The length of its tangent is
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Answers
Correct Question:
A tangent is drawn from a point at a distance of 17 cm to a circle of radius 8 cm. Find the length of the tangent.
Answer:
The length of the tangent is 15 cm.
Step-by-step-explanation:
NOTE: Refer to the attachment for the diagram.
In figure, O is the centre of circle.
Seg OQ is radius of circle.
∴ OQ = 8 cm. - - [ Given ]
PQ is a tangent to the circle at a distance of 17 cm.
∴ OP = 17 cm
Now, we know that,
Tangent drawn to a circle is always perpendicular to the radius of the circle.
∴ PQ ⊥ OQ
∴ In ΔOQP, m∠OQP = 90°
∴ ( OP )² = ( OQ )² + ( PQ )² - - [ Pythagors theorem ]
→ ( 17 )² = ( 8 )² + ( PQ )²
→ 289 = 64 + PQ²
→ PQ² = 289 - 64
→ PQ² = 225
→ PQ = √225 - - [ Taking square roots ]
∴ PQ = 15 cm
∴ The length of the tangent is 15 cm.
Additional Information:
1. Circle:
A geometric figure drawn from a fixed point having equal distances from the point is called circle.
2. Radius of circle:
The distance from the centre of circle to any point on the circle is called the radius of circle.
3. Diameter of circle:
The segment drawn from one point of a circle to another point which passes from the centre of circle is called diameter of circle.
4. Tangent:
A line segment which touches the circle in only one point externally is called the tangent.
5. Property of Tengemt and Radius:
Tangent drawn to a circle is always perpendicular to the radius of the circle.
the ans
very eazy
d=17cm
radius =8cm
pq=15cm