A circle with centre O and radius 8 cm is inscribed in a quadrilateral ABCD in which P, Q, R, S are the points of…

CBSE Class 10 Maths PYQ · Circles · Quad & Circle · 3 Marks · March 2024 · Standard

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1173 Marks · March 2024 · Standard

A circle with centre O and radius $8$ cm is inscribed in a quadrilateral ABCD in which P, Q, R, S are the points of contact as shown. If AD is perpendicular to DC, BC = $30$ cm and BS = $24$ cm, then find the length DC.

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Sol. Join OP and OQ.
BR = BS = $24$ cm
$\therefore CR = 6$ cm
$\Rightarrow CQ = 6$ cm
Also, DQ = OP = $8$ cm
Hence, DC = $8 + 6 = 14$ cm