P is the centre of the circle and seg QM is a tangent to the circle at point M . If QM =30,and PQ=34, then find the radius of the circle
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Answer:
Given, seg QM is tangent to the circle.
length of tangent QM = 30 units
PQ = 34 units ----- distance from point Q from centre P
Find Radius PM = ?
∵ sag QM is tangent
∴ PM ⊥ QM
∴ ∠PMQ = 90° ( ∵ Tangent at any point of a circle is perpendicular to the radius through point of contact)
so ΔPMQ is right-angle triangle
∴ Using Pythagorus theorem,
(PQ)² = (PM)² + (MQ)²
∴ (PM)² = (PQ)² - (MQ)²
= 34² - 30²
= 1156 - 900
∴ (PM)² = 256
∴ PM = 16 units
Radius PM = 16 units
Step-by-step explanation:
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