Draw a circle of radius 3.5 cm and construct a central angle of measure 80 $^{o}$ and an inscribed angled subtended by the same arc. Construct tangents at the points on the circle. Extend tangents to intersect. What do you observe?

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Solution

Draw a circle of radius $r = 3.5 c m$
Take a point $P$ on the circle and mark a chord of length $< 2 r$ and join $P Q$ and also join $P$ and $Q$ with center $O$
Take any point $S$ on the major sector and join $S$ with $P$ and $Q$
Taking $O P$ and $O Q$ as base, draw perpendiculars from $P$ and $Q$ respectively.
These perpendiculars meet at $T$
From measurement it is observed that
$∠ P O Q = 2 ∠ P S Q$

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Draw a circle of radius 3.5 cm and construct a central angle of measure 80o and an inscribed angled subtended by the same arc. Construct tangents at the points on the circle. Extend tangents to intersect. What do you observe?

Draw a circle of radius 3.5 cm and construct a central angle of measure 80 $^{o}$ and an inscribed angled subtended by the same arc. Construct tangents at the points on the circle. Extend tangents to intersect. What do you observe?