Find the 60th term of the AP 8, 10,12, ..., if it has a total of 60 terms and hence find the sum of its last 10 terms.
Prove that the length of tangents drawn from an external point to a circle is equal.
Given: TP and TQ are two tangent drawn from an external point T to the circle C (O, r).
To prove: TP = TQ
Construction: Join OT
Proof: we know that a tangent to the circle is perpendicular to the radius through the point of contanct.
∴ ∠OPT = ∠OQT = 90o
In Δ OPT and ΔOQT
OT = OT (common)
OP = OQ (radius of the circle)
∠OPT = ∠OQT (90o)
∴ ∠OPT = ∠OQT (RHS congruence criterion)
⇒ TP = TQ (CPCT)
Hence, the length of the tangents drawn from an external point to a circle is equal.
Construct a ΔABC in which AB = 6 cm, ∠A = 30o and ∠B = 60o. Construct another ΔAB'C' similar to ΔABC with base AB' = 8 cm
Find the values of k so that the area of the triangle with vertices (1,-1), (-4, 2k) and (-k, 5) is 24 sq. units