1. In the figure, PQ is a chord of a circle and PT is the tangent at P such that LQPT = 60°. Then find the measure of LPRQ.

Q

p

Solution.

Since OP is perpendicular to PT.

LOPT = 90°

LOPQ = 90°

- LQPT

LOPQ = 90 - 60 = 30°

.

In t:.OPQ, OP= OQ = r ( Radius of the circle )

LOPQ= LOQP = 30.

And,

LPOQ = 180 - LOPQ- LOQP

= 180° - 30° - 30°

= 120°

Also, reflex LPOQ = 360° - 120°

= 240°

Now, LPRQ = reflex LPOQ

= 12x 240°

= 120°

2. If the angle between two radii of a circle is 130°, then find the degree measure of the angle between the tangents at the ends

of the radii.

Solution.

It is already known that angle between two radii and the angle between the tangents at the ends of the radii are supplementary.

Hence, Angle between the tangents at the ends of the radii is 180° - 130° , i.e., 50°.

3. In the figure, if LAOS= 125°, then find the degree measure of L

Solution.

It is already known that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the

circle.

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NCERT SOLUTIONS CLASS 10 MATHS

CHAPTER 10 - CIRCLES TANGENTS PERPENDICULAR