QQuestion
The figure shows a circle of radius 9 cm with O as the centre. The diameter AB produced meets the tangent PQ at P. If PA = 24 cm, find the length of tangent PQ.
ICSEClass 10MathematicsCircles03 Mark2024 Moderate
✓Answer
Radius, OA = OB = 9 cm.
Therefore, diameter AB = OA + OB.
⇒ AB = 9 + 9
⇒ AB = 18 cm
Since PA = 24 cm:
PB = PA − AB
⇒ PB = 24 − 18
⇒ PB = 6 cm
By the tangent-secant theorem:
PQ² = PB × PA
⇒ PQ² = 6 × 24
⇒ PQ² = 144
⇒ PQ = √144
⇒ PQ = 12 cm
Therefore, the length of tangent PQ is 12 cm.
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