Math, asked by manishasuvarna63360, 1 year ago

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

Answers

Answered by varunmadkaikar
42

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:


Similar questions