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 .
Based on the above information, answer the question:
Q. Find the length of AR in terms of .
Given, AB = 7 m, BC = 15 m and AP = x m
Hence, AP = AR (Tangent drawn from an external point to the circle are equal in length)
AR = x m
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 .
Based on the above information, answer the question:
Q. Write the type of quadrilateral BQOR.
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.
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 .
Based on the above information, answer the question:
Q. Find the length PC in terms of and hence find the value of
(4.28)
Here, BC = 15 m
BQ = (7 – x)m
QC = 15 – (7 – x)
or, QC = (8 + x)m
Also, QC = PC (Tangents from an external points C to the circle)
i.e., PC = (8 + x)m
In right DABC, using Pythagoras theorem,
