Question

draw a pair of tangents to a circle of radius 5 centimetre which are inclined to each other at an angle of 60 degree

Answer 1

Hope it helps mate:)

Answer 2

$\huge\star{\purple{\underline{\underline{\mathfrak{Explanation:}}}}}$

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$\bold{\green{STEP-BY-STEP-CONSTRUCTION:}}$

• $\large{\pink\leadsto}$The tangents can be constructed as following:-

• $\large{\pink\leadsto}$Draw a circle of radius 5 cm and with centre as O.

• $\large{\pink\leadsto}$Take a point Q on the circumference of the circle and join OQ.

• $\large{\pink\leadsto}$Draw a perpendicular to QP at point Q.

• $\large{\pink\leadsto}$Draw a radius OR, making an angle of 120° (180° − 60°) with OQ.

• $\large{\pink\leadsto}$Draw a perpendicular to RP at point R.

• $\large{\pink\leadsto}$Now both the perpendiculars intersect at point P.

• $\large{\pink\leadsto}$Therefore, PQ and PR are the required tangents at an angle of 60°.

$\huge\star{\purple{\underline{\mathfrak{Justification:}}}}$

The construction can be justified by proving that ∠QPR = 60°

By our construction ∠OQP = 90°

∠ORP = 90° And ∠QOR = 120°

We know that the sum of all interior angles of a quadrilateral= 360°

∠OQP + ∠QOR + ∠ORP + ∠QPR=90° + 120° + 90° + ∠QPR= 360°

Therefore, ∠QPR = 60°

$\large\star{\pink{Hence,Justified!}}$