In the given figure, a circle is inscribed in a quadrilateral ABC… - Vidyadip

MCQ

In the given figure, a circle is inscribed in a quadrilateral ABCD touching its sides AB, BC, CD and AD at P, Q, R and S respectively. If the radius of the circle is 10cm, BC = 38cm, PB = 27cm and $\text{AD} \perp \text{CD}$ then the length of CD is:

A
11cm
B
15cm
C
20cm
✓
21cm

✓

Answer

Correct option: D.

21cm

We know that tangles from an external point to the circle are equal.
BQ = PB = 27cm
So, CQ = BC - BQ = 38 - 27 = 11cm
⇒ CR = CQ = 11cm
In quad. SORD,
$\angle\text{SDR}=90^\circ....(\therefore\text{AD}\perp\text{CD})$
$\Rightarrow\angle\text{OSD}=\angle\text{ORD}=90^\circ$
Also, OS = OR and SD = SR
So, quad. SORD is a square.
Thus, DR = SO = 10cm
Hence, CD = DR + CR = 10 + 11 = 21cn.

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