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$(ii) In a circle with centre O if \overline{O T} is the radial segment and \overleftrightarrow{P T Q} is the tangent line then(a) \overline{O T} \perp \overleftrightarrow{P Q} (b) \overline{O T} \perp \overleftrightarrow{P Q} (c) \overline{O T} / / \overleftrightarrow{P Q} (d) \overline{O T} is right bisector of \overleftrightarrow{P Q}$

$Example 1: \overline{A B} is a diameter of a given circle with centre O . Tangents are drawn at the end points A and B . Show that the two tangents are parallel.NOT FOR SALE - PESRP193Mathematics 10$

$2. The diameters of two concentric circles are 10 \mathrm{~cm} and 5 \mathrm{~cm} respectively. Look for the length of any chord of the outer circle which touches the inner one.(Hint) From the figure$

$2. The radius of a circle is 2.5 \mathrm{~cm} . \overline{A B} and \overline{C D} are two chords 3.9 \mathrm{~cm} apart. If m \overline{A B}=1.4 \mathrm{~cm} then measure the other chord.$

$(iv) In the adjacent figure find half the perimeter of circle with centre O if \pi \simeq 3.1416 and m \overline{O A}=20 \mathrm{~cm} .(a) 31.42 \mathrm{~cm} (b) 62.832 \mathrm{~cm} (c) 125.65 \mathrm{~cm} (d) 188.50 \mathrm{~cm}$

$(x) Tangents drawn at the ends of diameter of a circle are ...... to each other.(a) parallel(b) non-parallel(c) collinear(d) perpendicular$

$1. \overline{A B} and \overline{C D} are two equal chords in a circle with centre O . H and K are respectively the mid points of the chords. Prove that \overline{H K} makes equal angles with \overline{A B} and \overline{C D} .$