Justify and draw Q 2 Construct a tangent to a circle of radius 4 cm from a point on - Maths - Constructions

Question

Justify and draw
Q 2 Construct a tangent to a circle of radius 4 cm from a point on
the concentric circle of radius 6 cm and measure its length Also
verify the measurement by actual calculation

Abhishek Jha · Accepted Answer

Dear Student, Tangents on the given circle can be drawn as follows Step 1 Draw a circle of 4 cm radius with centre as O on the given plane Step 2 Draw a circle of 6 cm radius taking O as its centre Locate a point P on this circle and join OP Step 3 Bisect OP Let M be the mid-point of PO Step 4 Taking M as its centre and MO as its radius, draw a circle Let it intersect the given circle at the points Q and R Step 5 Join PQ and PR PQ and PR are the required tangents

It can be observed that PQ and PR are of length 4 47 cm each In ΔPQO, Since PQ is a tangent, ∠PQO = 90° PO = 6 cm QO = 4 cm Applying Pythagoras theorem in ΔPQO, we obtain PQ2 + QO2 = PQ2 PQ2 + (4)2 = (6)2 PQ2 + 16 = 36 PQ2 = 36 − 16 PQ2 = 20 PQ

PQ = 4 47 cm Justification The construction can be justified by proving that PQ and PR are the tangents to the circle (whose centre is O and radius is 4 cm) For this, let us join OQ and OR

∠PQO is an angle in the semi-circle We know that angle in a semi-circle is a right angle ∴ ∠PQO = 90° ⇒ OQ ⊥ PQ Since OQ is the radius of the circle, PQ has to be a tangent of the circle Similarly, PR is a tangent of the circle Regards

Justify and draw Q.2. Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

Justify and draw
Q.2. Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.