LINE DRAWN FROM TANGENT TO CIRCLE WORKSHEET

Work out the size of each angle marked with a letter. Give reasons for your answers.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 1 :

The length of the tangent drawn from a point 8 cm away from the center of a circle of radius 6 cm is

(a) 10 cm        (b) 5 cm      (c) √7 cm      (d) 2√7 cm

Solution

Problem 2 :

If tangents PA and PB from a point P to a circle with center O are inclined to each other at an angle of 80°, then ∠POA is

(a) 30⁰        (b) 60⁰      (c) 50⁰      (d) 100⁰

Solution

Problem 3 :

If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm then length of each tangent is --------------

Solution

Problem 4 :

If the angle between two tangents drawn from a point T to a circle of radius r and center O is 120⁰ then find the length of TP .

Solution

Problem 5 :

The length of a tangent from a point A at distance 5 cm from the center of the circle is 4 cm. Find the radius of the circle.

(a) 4 cm      (b) 3 cm      (c) 6 cm       (d) 5 cm

Solution

Problem 6 :

PQ is a chord of length 8 cm of a circle of radius 5 cm .The tangents at P and Q intersect at a point T . Find the length TP.

Solution