A circular pit was dug inside it such that it touches the walls AC, BC and AB at P, Q and R respectively such that, Write the type of quadrilateral BQOR.

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Solution

Q.
A backyard is in the shape of a triangle ABC with right angle at B. AB = 7 m and BC 15 m. A circular pit was dug inside it such that it touches the walls AC, BC and AB at P, Q and R respectively such that $A P = x m$ .

Based on the above information, answer the question:

Q. Write the type of quadrilateral BQOR.

Ans.
Since, AR = x m and AB = 7 m

$∴$ RB = (7 – x)m

Also, RB = BQ

(Tangents drawn from an external point to the circle)

OR = OQ (radii of circle)

$∠$ ORB = $∠$ OQB = 90° (Angle between radius and tangent)

Also, $∠$ RBQ = 90° (angle between the walls AB and BC)

Thus, $∠$ ROQ = 90°

Thus, BQOR is square.

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